Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2019, Volume 147, Issue 12, pp. 5417 - 5420

.... This answers negatively the question: Is every hypersurface with constant principal curvatures isoparametric?

MATHEMATICS | MATHEMATICS, APPLIED | Isoparametric hypersurface | constant principal curvatures

MATHEMATICS | MATHEMATICS, APPLIED | Isoparametric hypersurface | constant principal curvatures

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 4/2015, Volume 19, Issue 2, pp. 519 - 533

The goal of this paper is to prove null 2-type hypersurfaces with at most three distinct principal curvatures in a Euclidean space have constant mean curvature. 2010...

Tangents | Hypersurfaces | Mathematical constants | Euclidean space | Mathematical vectors | Curvature | Cylinders | Null 2-type submanifolds | Mean curvature vector | 3 Distinct principal curvatures | MATHEMATICS

Tangents | Hypersurfaces | Mathematical constants | Euclidean space | Mathematical vectors | Curvature | Cylinders | Null 2-type submanifolds | Mean curvature vector | 3 Distinct principal curvatures | MATHEMATICS

Journal Article

Kyushu journal of mathematics, ISSN 1340-6116, 2016, Volume 70, Issue 2, pp. 217 - 226

.... Here, a flat front is a flat surface (i.e., a surface where one of the principal curvatures is identically zero...

orientability | umbilic point | wave front | weak completeness, where one of the principal curvatures is constant | Weak completeness | Where one of the principal curvatures is constant | Wave front | Umbilic point | Orientability | MATHEMATICS | FLAT MOBIUS STRIPS | 3-SPACE | SINGULARITIES | HYPERBOLIC SPACE | GEODESICS | weak completeness | where one of the principal curvatures is constant | SURFACES

orientability | umbilic point | wave front | weak completeness, where one of the principal curvatures is constant | Weak completeness | Where one of the principal curvatures is constant | Wave front | Umbilic point | Orientability | MATHEMATICS | FLAT MOBIUS STRIPS | 3-SPACE | SINGULARITIES | HYPERBOLIC SPACE | GEODESICS | weak completeness | where one of the principal curvatures is constant | SURFACES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2012, Volume 140, Issue 12, pp. 4323 - 4335

... → R whose gradient decays uniformly faster than 1/r. The divergence theorem then yields a pair of integral equations for the normal curvatures of these graphs, which establish some weaker forms of the conjecture...

Circles | Hypersurfaces | Mathematical constants | Mathematical functions | Mathematical surfaces | Divergence theorem | Curvature | Spherical coordinates | Polar coordinate graphs | Parallel surface | Principal line | Loewner conjecture | Carathéodory conjecture | Möbius inversion | Umbilical point | MATHEMATICS, APPLIED | parallel surface | PROOF | UMBILIC POINTS | Mobius inversion | MATHEMATICS | SUPPOSITION | divergence theorem | HYPERSURFACES | SURFACE | Caratheodory conjecture | principal line | LOEWNER | INDEX

Circles | Hypersurfaces | Mathematical constants | Mathematical functions | Mathematical surfaces | Divergence theorem | Curvature | Spherical coordinates | Polar coordinate graphs | Parallel surface | Principal line | Loewner conjecture | Carathéodory conjecture | Möbius inversion | Umbilical point | MATHEMATICS, APPLIED | parallel surface | PROOF | UMBILIC POINTS | Mobius inversion | MATHEMATICS | SUPPOSITION | divergence theorem | HYPERSURFACES | SURFACE | Caratheodory conjecture | principal line | LOEWNER | INDEX

Journal Article

Results in Mathematics, ISSN 1422-6383, 6/2015, Volume 67, Issue 3, pp. 457 - 470

... } and $${n \geq 2}$$ n ≥ 2 , having two distinct principal curvatures with multiplicity p and n − p...

53C20 | Primary 53C42 | normalized scalar curvature | 53C50 | totally umbilical hypersurfaces | mean curvature | Mathematics, general | Secondary 53A10 | Mathematics | isoparametric hypersurfaces | Space forms | Totally umbilical hypersurfaces | Mean curvature | Isoparametric hypersurfaces | Normalized scalar curvature | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANT SCALAR CURVATURE | LINEAR WEINGARTEN HYPERSURFACES | MINIMAL HYPERSURFACES | RIEMANNIAN-MANIFOLDS

53C20 | Primary 53C42 | normalized scalar curvature | 53C50 | totally umbilical hypersurfaces | mean curvature | Mathematics, general | Secondary 53A10 | Mathematics | isoparametric hypersurfaces | Space forms | Totally umbilical hypersurfaces | Mean curvature | Isoparametric hypersurfaces | Normalized scalar curvature | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANT SCALAR CURVATURE | LINEAR WEINGARTEN HYPERSURFACES | MINIMAL HYPERSURFACES | RIEMANNIAN-MANIFOLDS

Journal Article

Collectanea Mathematica, ISSN 0010-0757, 9/2016, Volume 67, Issue 3, pp. 379 - 397

Our purpose in this paper is to study the geometry of complete linear Weingarten spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space...

53C20 | Primary 53C42 | 53C50 | Locally symmetric Lorentz spaces | Complete linear Weingarten spacelike hypersurfaces | Mathematics | Geometry | Algebra | Einstein spacetimes | Analysis | Secondary 53A10 | Applications of Mathematics | Isoparametric hypersurfaces | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | DE-SITTER SPACE | MAXIMAL SPACE | MANIFOLDS | GEOMETRY

53C20 | Primary 53C42 | 53C50 | Locally symmetric Lorentz spaces | Complete linear Weingarten spacelike hypersurfaces | Mathematics | Geometry | Algebra | Einstein spacetimes | Analysis | Secondary 53A10 | Applications of Mathematics | Isoparametric hypersurfaces | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | DE-SITTER SPACE | MAXIMAL SPACE | MANIFOLDS | GEOMETRY

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 12/2014, Volume 46, Issue 4, pp. 351 - 359

In this paper we write some differential formulas involving the high-order Levi curvatures of a real hypersurface in a complex space form...

Geometry | Primary 32V40 | Statistics for Business/Economics/Mathematical Finance/Insurance | Pseudoconvexity | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Group Theory and Generalizations | Secondary 32T99 | Complex space form | REINHARDT DOMAINS | THEOREM | FORM | C-2 | HOPF HYPERSURFACES | SYMMETRY RESULT | MATHEMATICS | CONSTANT PRINCIPAL CURVATURES | COMPLEX PROJECTIVE-SPACE | HYPERBOLIC SPACE | REAL HYPERSURFACES | Studies | Theorems | Mathematical analysis | Curvature | Classification

Geometry | Primary 32V40 | Statistics for Business/Economics/Mathematical Finance/Insurance | Pseudoconvexity | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Group Theory and Generalizations | Secondary 32T99 | Complex space form | REINHARDT DOMAINS | THEOREM | FORM | C-2 | HOPF HYPERSURFACES | SYMMETRY RESULT | MATHEMATICS | CONSTANT PRINCIPAL CURVATURES | COMPLEX PROJECTIVE-SPACE | HYPERBOLIC SPACE | REAL HYPERSURFACES | Studies | Theorems | Mathematical analysis | Curvature | Classification

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 6/2018, Volume 197, Issue 3, pp. 703 - 720

In this paper, I study the isoparametric hypersurfaces in a Randers sphere $$(S^n,F)$$ (Sn,F) of constant flag curvature, with the navigation datum...

53C42 | Navigation | Randers sphere of constant flag curvature | Mathematics, general | Mathematics | Isoparametric function | Isoparametric hypersurface | 53C60 | Homogeneous hypersurface | 22E46 | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | FAMILIES | 4 PRINCIPAL CURVATURES | RIEMANNIAN-MANIFOLDS

53C42 | Navigation | Randers sphere of constant flag curvature | Mathematics, general | Mathematics | Isoparametric function | Isoparametric hypersurface | 53C60 | Homogeneous hypersurface | 22E46 | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | FAMILIES | 4 PRINCIPAL CURVATURES | RIEMANNIAN-MANIFOLDS

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 2011, Volume 29, Issue 1, pp. S65 - S70

We present the motivation and current state of the classification problem of real hypersurfaces with constant principal curvatures in complex space forms...

Homogeneous hypersurfaces | Hopf hypersurfaces | Constant principal curvatures | Secondary | Primary | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTIVE-SPACE | SPHERES | ISOPARAMETRIC HYPERSURFACES | COHOMOGENEITY ONE ACTIONS | HYPERBOLIC SPACES

Homogeneous hypersurfaces | Hopf hypersurfaces | Constant principal curvatures | Secondary | Primary | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTIVE-SPACE | SPHERES | ISOPARAMETRIC HYPERSURFACES | COHOMOGENEITY ONE ACTIONS | HYPERBOLIC SPACES

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2010, Volume 60, Issue 1, pp. 43 - 52

We investigate complete spacelike hypersurfaces in Lorentz–Minkowski space with two distinct principal curvatures and constant m th mean curvature. By using...

Spacelike hypersurface | Principal curvature | Mean curvature | Lorentz–Minkowski space | Lorentz-Minkowski space | MATHEMATICS, APPLIED | CONSTANT SCALAR CURVATURE | SITTER SPACE | PHYSICS, MATHEMATICAL

Spacelike hypersurface | Principal curvature | Mean curvature | Lorentz–Minkowski space | Lorentz-Minkowski space | MATHEMATICS, APPLIED | CONSTANT SCALAR CURVATURE | SITTER SPACE | PHYSICS, MATHEMATICAL

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2011, Volume 60, Issue 3, pp. 859 - 882

We classify real hypersurfaces in complex space forms with constant principal curvatures and whose Hopf vector field has two nontrivial projections onto the principal curvature spaces...

Tangents | Mathematical theorems | Algebra | Hypersurfaces | Vector fields | Mathematical constants | Curvature | Unit vectors | Projection of vectors | Homogeneous hypersurfaces | Constant principal curvatures | Hopf hypersurfaces | homogeneous hypersurfaces | MATHEMATICS | PROJECTIVE-SPACE | SPHERES | ISOPARAMETRIC HYPERSURFACES | COHOMOGENEITY ONE ACTIONS | constant principal curvatures | HYPERBOLIC SPACES

Tangents | Mathematical theorems | Algebra | Hypersurfaces | Vector fields | Mathematical constants | Curvature | Unit vectors | Projection of vectors | Homogeneous hypersurfaces | Constant principal curvatures | Hopf hypersurfaces | homogeneous hypersurfaces | MATHEMATICS | PROJECTIVE-SPACE | SPHERES | ISOPARAMETRIC HYPERSURFACES | COHOMOGENEITY ONE ACTIONS | constant principal curvatures | HYPERBOLIC SPACES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2007, Volume 135, Issue 10, pp. 3349 - 3358

We classify real hypersurfaces with constant principal curvatures in the complex hyperbolic plane...

Tangents | Maps | Unit normal vectors | Hypersurfaces | Vector fields | Mathematical constants | Mathematics | Mathematical vectors | Curvature | Unit vectors | Homogeneous hypersurfaces | Constant principal curvatures | homogeneous hypersurfaces | MATHEMATICS | COHOMOGENEITY ONE ACTIONS | MATHEMATICS, APPLIED | constant principal curvatures | SPACES

Tangents | Maps | Unit normal vectors | Hypersurfaces | Vector fields | Mathematical constants | Mathematics | Mathematical vectors | Curvature | Unit vectors | Homogeneous hypersurfaces | Constant principal curvatures | homogeneous hypersurfaces | MATHEMATICS | COHOMOGENEITY ONE ACTIONS | MATHEMATICS, APPLIED | constant principal curvatures | SPACES

Journal Article

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 10/2015, Volume 56, Issue 2, pp. 641 - 653

We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms...

Geometry | 53C42 | Algebra | Convex and Discrete Geometry | Algebraic Geometry | Constant principal curvature | Mathematics | Pseudo-Riemannian space forms

Geometry | 53C42 | Algebra | Convex and Discrete Geometry | Algebraic Geometry | Constant principal curvature | Mathematics | Pseudo-Riemannian space forms

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 6/2018, Volume 15, Issue 3, pp. 1 - 12

We establish an inequality among the Ricci curvature, the squared mean curvature, and the normal curvature for real hypersurfaces in complex space forms...

Primary 53C42 | normal curvature | Secondary 53B25 | Real hypersurfaces | Ricci curvature | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANT PRINCIPAL CURVATURES

Primary 53C42 | normal curvature | Secondary 53B25 | Real hypersurfaces | Ricci curvature | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANT PRINCIPAL CURVATURES

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 2011, Volume 29, Issue 3, pp. 279 - 291

We investigate complete spacelike hypersurfaces in a de Sitter space with two distinct principal curvatures and constant m-th mean curvature. By using...

Spacelike hypersurface | Principal curvature | Lorentzian space form | Mean curvature | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | Space like hypersurface | Mathematical analysis | Curvature | Differential geometry | Classification | Images | Cylinders

Spacelike hypersurface | Principal curvature | Lorentzian space form | Mean curvature | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | Space like hypersurface | Mathematical analysis | Curvature | Differential geometry | Classification | Images | Cylinders

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 304, pp. 434 - 493

...)-dimensional Minkowski space, provided D is contained in the future cone over a point. Namely, it is possible to find a smooth convex Cauchy surface with prescribed curvature function on the image of the Gauss map...

Minkowski space | Constant curvature surfaces | Monge–Ampère equation | Universal Teichmüller theory | MATHEMATICS | Monge-Ampere equation | HYPERSURFACES | GAUSS CURVATURE | Universal Teichmuller theory | Mathematics

Minkowski space | Constant curvature surfaces | Monge–Ampère equation | Universal Teichmüller theory | MATHEMATICS | Monge-Ampere equation | HYPERSURFACES | GAUSS CURVATURE | Universal Teichmuller theory | Mathematics

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 2/2012, Volume 156, Issue 1, pp. 31 - 47

... (or, equivalently, the infimum of the squared norm of the second fundamental form) of a constant mean curvature hypersurface with two principal curvatures immersed into a Riemannian space form of constant curvature...

Geometry | Omori-Yau maximum principle | 53C42 | Scalar curvature | 53C40 | Constant mean curvature | Second fundamental form | Ricci curvature | Mathematics | MATHEMATICS | 2 PRINCIPAL CURVATURES | THEOREM | SPHERE | RIGIDITY | RIEMANNIAN MANIFOLDS | MINIMAL HYPERSURFACES

Geometry | Omori-Yau maximum principle | 53C42 | Scalar curvature | 53C40 | Constant mean curvature | Second fundamental form | Ricci curvature | Mathematics | MATHEMATICS | 2 PRINCIPAL CURVATURES | THEOREM | SPHERE | RIGIDITY | RIEMANNIAN MANIFOLDS | MINIMAL HYPERSURFACES

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 04/2020, Volume 293, Issue 4, pp. 735 - 753

We classify all rotational surfaces in Euclidean space whose principal curvatures κ1...

53C42 | phase plane | 53A10 | rotational surface | principal curvature | Weingarten surface | MATHEMATICS | CONSTANT MEAN-CURVATURE | WEINGARTEN SURFACES

53C42 | phase plane | 53A10 | rotational surface | principal curvature | Weingarten surface | MATHEMATICS | CONSTANT MEAN-CURVATURE | WEINGARTEN SURFACES

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 10/2014, Volume 24, Issue 4, pp. 1882 - 1890

Let M⊂S 4 be a complete orientable hypersurface with constant scalar curvature. For any v∈R 5, let us define the two real functions...

Abstract Harmonic Analysis | Constant scalar curvature | 53C42 | Principal curvature | 53A10 | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Mathematics | Sectional curvature | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS

Abstract Harmonic Analysis | Constant scalar curvature | 53C42 | Principal curvature | 53A10 | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Mathematics | Sectional curvature | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS

Journal Article

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Full Text
A complete classification of Blaschke parallel submanifolds with vanishing Möbius form

Science China Mathematics, ISSN 1674-7283, 07/2017, Volume 60, Issue 7, pp. 1281 - 1310

The Blaschke tensor and the Mobius form are two of the fundamental invariants in the Mobius geometry of submanifolds; an umbilic-free immersed submanifold in...

parallel mean curvature vector | parallel Blaschke tensor | constant scalar curvature | vanishing Möbius form | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | vanishing Mobius form | SM+1 | ISOPARAMETRIC HYPERSURFACES | SCALAR CURVATURE | IMMERSED HYPERSURFACES | UNIT-SPHERE | MATHEMATICS | S-N | MEAN-CURVATURE | GEOMETRY

parallel mean curvature vector | parallel Blaschke tensor | constant scalar curvature | vanishing Möbius form | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | vanishing Mobius form | SM+1 | ISOPARAMETRIC HYPERSURFACES | SCALAR CURVATURE | IMMERSED HYPERSURFACES | UNIT-SPHERE | MATHEMATICS | S-N | MEAN-CURVATURE | GEOMETRY

Journal Article

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