Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2002, Volume 354, Issue 2, pp. 571 - 612

An isometric action of a compact Lie group on a Riemannian manifold is called hyperpolar if there exists a closed, connected submanifold that is flat in the...

Isotropy | Algebra | Mathematical theorems | Adjoints | Lie groups | Subalgebras | Automorphisms | Algebraic conjugates | Symmetry | Hyperpolar actions | Symmetric spaces | Cohomogeneity one actions | Compact Lie groups | MATHEMATICS | compact Lie groups | cohomogeneity one actions | hyperpolar actions | symmetric spaces | SPACES

Isotropy | Algebra | Mathematical theorems | Adjoints | Lie groups | Subalgebras | Automorphisms | Algebraic conjugates | Symmetry | Hyperpolar actions | Symmetric spaces | Cohomogeneity one actions | Compact Lie groups | MATHEMATICS | compact Lie groups | cohomogeneity one actions | hyperpolar actions | symmetric spaces | SPACES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2019, Volume 470, Issue 1, pp. 201 - 217

Let G/H be a connected, simply connected homogeneous space of a compact Lie group G. We study G-invariant quasi-Einstein metrics on the cohomogeneity one...

Quasi-Einstein metrics | Smoothness conditions | Cohomogeneity-one manifolds | Dirichlet conditions | MATHEMATICS | MATHEMATICS, APPLIED | ONE MANIFOLDS | NONEXISTENCE | DIRICHLET PROBLEM | BOUNDARY | RICCI CURVATURE

Quasi-Einstein metrics | Smoothness conditions | Cohomogeneity-one manifolds | Dirichlet conditions | MATHEMATICS | MATHEMATICS, APPLIED | ONE MANIFOLDS | NONEXISTENCE | DIRICHLET PROBLEM | BOUNDARY | RICCI CURVATURE

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 7/2017, Volume 52, Issue 1, pp. 99 - 128

Let M be a cohomogeneity one manifold of a compact semisimple Lie group G with one singular orbit $$S_0 = G/H$$ S 0 = G / H . Then M is G-diffeomorphic to the...

Flag manifolds | Theoretical, Mathematical and Computational Physics | 53C55 | 17B08 | Mathematics | Kähler–Einstein manifolds | Cohomogeneity one manifolds | Geometry | 17B22 | 32V99 | Dynkin diagrams | Analysis | 32Q20 | 17B10 | Group Theory and Generalizations | CR manifolds | MATHEMATICS | Kahler-Einstein manifolds | METRICS | HOMOGENEOUS SPACES | COMPACT COMPLEX-MANIFOLDS | Bundling | Manifolds | Invariants | Lie groups | Painting

Flag manifolds | Theoretical, Mathematical and Computational Physics | 53C55 | 17B08 | Mathematics | Kähler–Einstein manifolds | Cohomogeneity one manifolds | Geometry | 17B22 | 32V99 | Dynkin diagrams | Analysis | 32Q20 | 17B10 | Group Theory and Generalizations | CR manifolds | MATHEMATICS | Kahler-Einstein manifolds | METRICS | HOMOGENEOUS SPACES | COMPACT COMPLEX-MANIFOLDS | Bundling | Manifolds | Invariants | Lie groups | Painting

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2016, Volume 441, Issue 2, pp. 624 - 634

In this paper, we study S-curvature of cohomogeneity one Randers spaces with orbit space S1. In particular, we present an explicit coordinate-free formula of...

Cohomogeneity one space | S-curvature | Randers metric | Invariant vector field

Cohomogeneity one space | S-curvature | Randers metric | Invariant vector field

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 4/2018, Volume 288, Issue 3, pp. 829 - 853

We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the...

57M60 | 57S25 | Cohomogeneity one | Group action | Smoothing | 57S10 | 57N15 | Mathematics, general | Topological manifold | Mathematics | 57R10 | LOW DIMENSIONS | SPACES | SPHERES | CLASSIFICATION | FORMULA | MATHEMATICS | INDEX | POSITIVE RICCI CURVATURE | GEOMETRY | Algebra

57M60 | 57S25 | Cohomogeneity one | Group action | Smoothing | 57S10 | 57N15 | Mathematics, general | Topological manifold | Mathematics | 57R10 | LOW DIMENSIONS | SPACES | SPHERES | CLASSIFICATION | FORMULA | MATHEMATICS | INDEX | POSITIVE RICCI CURVATURE | GEOMETRY | Algebra

Journal Article

Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 3/2019, Volume 50, Issue 1, pp. 291 - 313

We characterize centroaffine surfaces of cohomogeneity one which have vanishing Tchebychev vector fields. Moreover, we classify centroaffine minimal surfaces...

Centroaffine minimal surfaces | Cohomogeneity one | 53A15 | Theoretical, Mathematical and Computational Physics | Proper affine spheres | Mathematics, general | Mathematics | Rotation surfaces | 53A05 | MATHEMATICS

Centroaffine minimal surfaces | Cohomogeneity one | 53A15 | Theoretical, Mathematical and Computational Physics | Proper affine spheres | Mathematics, general | Mathematics | Rotation surfaces | 53A05 | MATHEMATICS

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 03/2017, Volume 14, Issue 3

The Page metric on CP2# CP2 is a cohomogeneity one Einstein-Riemannian metric, and is the only known cohomogeneity one Einstein-Riemannian metric on compact...

Cohomogeneity one manifold | Einstein-Randers metric | invariant vector field | ONE MANIFOLDS | SPACES | CURVATURE | PHYSICS, MATHEMATICAL

Cohomogeneity one manifold | Einstein-Randers metric | invariant vector field | ONE MANIFOLDS | SPACES | CURVATURE | PHYSICS, MATHEMATICAL

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2007, Volume 359, Issue 7, pp. 3425 - 3438

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the...

Equivalence relation | Isotropy | Riemann manifold | Algebra | Subalgebras | Hypersurfaces | Vector spaces | Symmetry | Normal spaces | homogeneous hypersurfaces | CO-HOMOLOGY | MATHEMATICS | symmetric spaces | hyperbolic spaces | cohomogeneity one actions | GEOMETRY

Equivalence relation | Isotropy | Riemann manifold | Algebra | Subalgebras | Hypersurfaces | Vector spaces | Symmetry | Normal spaces | homogeneous hypersurfaces | CO-HOMOLOGY | MATHEMATICS | symmetric spaces | hyperbolic spaces | cohomogeneity one actions | GEOMETRY

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 12/2019, Volume 203, Issue 1, pp. 205 - 223

We compute the rational Borel equivariant cohomology ring of a cohomogeneity-one action of a compact Lie group.

Cohomogeneity-one Lie group actions on topological manifolds | Convex and Discrete Geometry | Lie groups | Equivariant cohomology | Algebraic Geometry | Mathematics | Hyperbolic Geometry | Projective Geometry | Topology | Differential Geometry

Cohomogeneity-one Lie group actions on topological manifolds | Convex and Discrete Geometry | Lie groups | Equivariant cohomology | Algebraic Geometry | Mathematics | Hyperbolic Geometry | Projective Geometry | Topology | Differential Geometry

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 10/2017, Volume 184, Issue 2, pp. 185 - 200

We study isometric cohomogeneity one actions on the $$(n+1)$$ ( n + 1 ) -dimensional Minkowski space $$\mathbb {L}^{n+1}$$ L n + 1 up to orbit-equivalence. We...

Minkowski space | Mathematics, general | Mathematics | 53C50 | Cohomogeneity one actions | Parabolic subgroups | MATHEMATICS | COMPACT LORENTZ MANIFOLD | ISOMETRY GROUP

Minkowski space | Mathematics, general | Mathematics | 53C50 | Cohomogeneity one actions | Parabolic subgroups | MATHEMATICS | COMPACT LORENTZ MANIFOLD | ISOMETRY GROUP

Journal Article

JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, ISSN 1812-9471, 2019, Volume 15, Issue 2, pp. 155 - 169

In the paper, we give a classification of closed and connected Lie groups, up to conjugacy in Iso(R-1,R-2), acting by cohomogeneity one on the three...

MATHEMATICS | MATHEMATICS, APPLIED | DE-SITTER SPACE | ISOMETRY GROUP | Minkowski space | cohomogeneity one | MANIFOLDS | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry

MATHEMATICS | MATHEMATICS, APPLIED | DE-SITTER SPACE | ISOMETRY GROUP | Minkowski space | cohomogeneity one | MANIFOLDS | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 7/2018, Volume 54, Issue 1, pp. 155 - 171

Let $$G{/}H$$ G/H be a compact homogeneous space, and let $$\hat{g}_0$$ g^0 and $$\hat{g}_1$$ g^1 be G-invariant Riemannian metrics on $$G/H$$ G/H . We...

Geometry | Einstein metrics | Mathematical Physics | Analysis | Dirichlet conditions | Global Analysis and Analysis on Manifolds | Mathematics | Differential Geometry | Cohomogeneity one manifolds | MATHEMATICS | BOUNDARY | RICCI CURVATURE | Manifolds | Isotropy | Dirichlet problem | Invariants

Geometry | Einstein metrics | Mathematical Physics | Analysis | Dirichlet conditions | Global Analysis and Analysis on Manifolds | Mathematics | Differential Geometry | Cohomogeneity one manifolds | MATHEMATICS | BOUNDARY | RICCI CURVATURE | Manifolds | Isotropy | Dirichlet problem | Invariants

Journal Article

Results in Mathematics, ISSN 1422-6383, 09/2017, Volume 72, Issue 1-2, pp. 515 - 536

In this paper we classify, up to orbit equivalence, cohomogeneity one actions of connected closed Lie subgroups of U(1, n) on the (2n + 1)-dimensional anti de...

Cohomogeneity one actions | anti de Sitter spacetime | parabolic subgroups | MATHEMATICS | MATHEMATICS, APPLIED | HYPERSURFACES | ISOMETRY GROUP

Cohomogeneity one actions | anti de Sitter spacetime | parabolic subgroups | MATHEMATICS | MATHEMATICS, APPLIED | HYPERSURFACES | ISOMETRY GROUP

Journal Article

Topology and its Applications, ISSN 0166-8641, 03/2017, Volume 218, pp. 93 - 96

We show that for any cohomogeneity-one continuous action of a compact connected Lie group G on a closed topological manifold the equivariant cohomology...

Cohomogeneity one group actions on topological manifolds | Cohen–Macaulay rings | Compact Lie groups | Equivariant cohomology | MATHEMATICS | MATHEMATICS, APPLIED | Cohen-Macaulay rings

Cohomogeneity one group actions on topological manifolds | Cohen–Macaulay rings | Compact Lie groups | Equivariant cohomology | MATHEMATICS | MATHEMATICS, APPLIED | Cohen-Macaulay rings

Journal Article

15.
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Invariant Ricci-flat metrics of cohomogeneity one with Wallach spaces as principal orbits

Annals of Global Analysis and Geometry, ISSN 0232-704X, 9/2019, Volume 56, Issue 2, pp. 361 - 401

We construct a continuous 1-parameter family of smooth complete Ricci-flat metrics of cohomogeneity one on vector bundles over $$\mathbb {CP}^2$$ CP 2 ,...

Geometry | G_{2}$$ G 2 holonomy | Mathematical Physics | Cohomogeneity one manifold | Analysis | Global Analysis and Analysis on Manifolds | Noncompact Ricci-flat manifold | Mathematics | Differential Geometry | MATHEMATICS | SOLITONS | G holonomy | EINSTEIN-METRICS | MANIFOLDS | Orbits | Parameters

Geometry | G_{2}$$ G 2 holonomy | Mathematical Physics | Cohomogeneity one manifold | Analysis | Global Analysis and Analysis on Manifolds | Noncompact Ricci-flat manifold | Mathematics | Differential Geometry | MATHEMATICS | SOLITONS | G holonomy | EINSTEIN-METRICS | MANIFOLDS | Orbits | Parameters

Journal Article

Axioms, ISSN 2075-1680, 12/2018, Volume 8, Issue 1, p. 2

This paper is one of a series in which we generalize our earlier results on the equivalence of existence of Calabi extremal metrics to the geodesic stability...

Cohomogeneity one | Einstein metrics | Fibration | Ricci curvature | Kähler manifolds | Sasakian-Einstein | Almost-homogeneous | Semisimple Lie group | Calabi-Yau metrics | semisimple Lie group | Calabi–Yau metrics | Sasakian–Einstein | almost-homogeneous | cohomogeneity one | fibration

Cohomogeneity one | Einstein metrics | Fibration | Ricci curvature | Kähler manifolds | Sasakian-Einstein | Almost-homogeneous | Semisimple Lie group | Calabi-Yau metrics | semisimple Lie group | Calabi–Yau metrics | Sasakian–Einstein | almost-homogeneous | cohomogeneity one | fibration

Journal Article

数理解析研究所講究録, ISSN 1880-2818, 01/2009, Volume 1623, pp. 102 - 110

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 08/2016, Volume 106, pp. 305 - 313

The aim of this paper is to prove that there exists no cohomogeneity one G-invariant proper biharmonic hypersurface into the Euclidean space Rn, where G...

Biharmonic immersions | Equivariant differential geometry | Biharmonic maps | Transformation groups | Cohomogeneity one hypersurfaces | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | SPHERES | PHYSICS, MATHEMATICAL | VECTOR | SUBMANIFOLDS | MEAN-CURVATURE | IMMERSIONS | RIEMANNIAN-MANIFOLDS | Mathematics - Differential Geometry

Biharmonic immersions | Equivariant differential geometry | Biharmonic maps | Transformation groups | Cohomogeneity one hypersurfaces | MATHEMATICS, APPLIED | DISTINCT PRINCIPAL CURVATURES | SPHERES | PHYSICS, MATHEMATICAL | VECTOR | SUBMANIFOLDS | MEAN-CURVATURE | IMMERSIONS | RIEMANNIAN-MANIFOLDS | Mathematics - Differential Geometry

Journal Article

19.
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Cohomogeneity one three dimensional anti-de Sitter space, proper and nonproper actions

Differential Geometry and its Applications, ISSN 0926-2245, 04/2015, Volume 39, pp. 93 - 112

In this paper we give a classification of closed and connected Lie groups, up to conjugacy in Iso(adS3), acting by cohomogeneity one on the three dimensional...

Anti de Sitter space | Cohomogeneity one | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | ONE MANIFOLDS | CURVATURE | Mathematics - Differential Geometry

Anti de Sitter space | Cohomogeneity one | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | ONE MANIFOLDS | CURVATURE | Mathematics - Differential Geometry

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2016, Volume 195, Issue 4, pp. 1269 - 1286

Let M be a domain enclosed between two principal orbits on a cohomogeneity one manifold $$M_1$$ M 1 . Suppose that T and R are symmetric invariant...

53C20 | 53B20 | Cohomogeneity one | 58J32 | Ricci curvature | Mathematics, general | Dirichlet problem | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | EINSTEIN EQUATIONS | METRICS | BOUNDARY

53C20 | 53B20 | Cohomogeneity one | 58J32 | Ricci curvature | Mathematics, general | Dirichlet problem | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | EINSTEIN EQUATIONS | METRICS | BOUNDARY

Journal Article

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