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Boletim da Sociedade Brasileira de Matemática, ISSN 1678-7714, 05/2018, Volume 50, Issue 1, pp. 37 - 65

A framed surface is a smooth surface in the Euclidean space with a moving frame. The framed surfaces may have singularities...

57R45 | Theoretical, Mathematical and Computational Physics | Framed surface | Singular point | Frontal | 58K05 | Mathematics, general | Mathematics | 53A05 | Basic invariant | Curvature | Physical Sciences | Science & Technology | Euclidean geometry | Euclidean space | Singularities | Invariants

57R45 | Theoretical, Mathematical and Computational Physics | Framed surface | Singular point | Frontal | 58K05 | Mathematics, general | Mathematics | 53A05 | Basic invariant | Curvature | Physical Sciences | Science & Technology | Euclidean geometry | Euclidean space | Singularities | Invariants

Journal Article

2017, Graduate studies in mathematics, ISBN 9781470429522, Volume 178, xvi, 414 pages

Lorentz metrics, indefinite metrics | Classical differential geometry | Vector analysis | Differential geometry | Global analysis, analysis on manifolds | Local differential geometry | Surfaces in Euclidean space | Differential forms | Noncompact transformation groups | Exterior differential systems (Cartan theory) | Projective differential geometry | Frames (Vector analysis) | Homogeneous spaces | Geometry, Differential | Topological groups, Lie groups | Affine differential geometry | Local submanifolds | General theory of differentiable manifolds | Mathematical physics | Exterior differential systems | Differential invariants (local theory), geometric objects | Curves in Euclidean space

Book

The Journal of geometric analysis, ISSN 1050-6926, 1/2017, Volume 27, Issue 1, pp. 817 - 841

...J Geom Anal (2017) 27:817–841
DOI 10.1007/s12220-016-9699-6
Generalizations of the Choe–Hoppe Helicoid and
Clifford Cones in Euclidean Space
Eunjoo Lee 1...

53A10 | Clifford cones | Clifford tori | 49Q05 | Mathematics | Minimal submanifolds | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Helicoids | Differential Geometry | Dynamical Systems and Ergodic Theory | Physical Sciences | Science & Technology | Toruses | Euclidean geometry | Euclidean space | Cones | Minimal surfaces | Manifolds (mathematics)

53A10 | Clifford cones | Clifford tori | 49Q05 | Mathematics | Minimal submanifolds | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Helicoids | Differential Geometry | Dynamical Systems and Ergodic Theory | Physical Sciences | Science & Technology | Toruses | Euclidean geometry | Euclidean space | Cones | Minimal surfaces | Manifolds (mathematics)

Journal Article

Resultate der Mathematik, ISSN 1420-9012, 11/2019, Volume 75, Issue 1, pp. 1 - 22

A translation surface of Euclidean space $${\mathbb {R}}^3$$
R3
is the sum of two regular curves $$\alpha $$
α
and $$\beta $$
β...

Primary 53A10 | minimal surface | Translation surface | darboux surface | Secondary 53C42 | Mathematics, general | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Mathematics - Differential Geometry

Primary 53A10 | minimal surface | Translation surface | darboux surface | Secondary 53C42 | Mathematics, general | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Mathematics - Differential Geometry

Journal Article

Rendiconti del Circolo matematico di Palermo, ISSN 0009-725X, 04/2018, Volume 67, Issue 1, pp. 59 - 66

...Rend. Circ. Mat. Palermo, II. Ser (2018) 67:59–66
https://doi.org/10.1007/s12215-016-0292-4
Rotational surfaces in higher dimensional Euclidean
spaces
K...

Generalized tractrix | rotational surface | Gaussian curvature | Beltrami surface

Generalized tractrix | rotational surface | Gaussian curvature | Beltrami surface

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2017, Volume 54, Issue 3, pp. 999 - 1013

In the present study we consider the generalized rotational surfaces in Euclidean spaces...

Generalized tractrix | Gaussian curvature | Beltrami surface | Rotational surface | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Generalized tractrix | Gaussian curvature | Beltrami surface | Rotational surface | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Acta et commentationes Universitatis Tartuensis de mathematica, ISSN 1406-2283, 2016, Volume 20, Issue 2, pp. 123 - 133

... surfaces in 4-dimensional Euclidean space Kadri Arslan, Bengü Bayram, Betül Bulca, and Günay Öztürk Abstract. We consider translation surfaces in Euclidean spaces...

Second fundamental map | Translation surface | Gaussian curvature | Mean curvature

Second fundamental map | Translation surface | Gaussian curvature | Mean curvature

Journal Article

Journal of geometry, ISSN 1420-8997, 12/2018, Volume 110, Issue 1, pp. 1 - 7

Understanding and finding of general algebraic constant mean curvature surfaces in the Euclidean spaces is a hard open problem...

Geometry | 53C42 | 53A10 | algebraic surfaces | Mathematics | Constant mean curvature | Hyperspaces | Euclidean space | Polynomials | Algebra | Curvature | Cylinders

Geometry | 53C42 | 53A10 | algebraic surfaces | Mathematics | Constant mean curvature | Hyperspaces | Euclidean space | Polynomials | Algebra | Curvature | Cylinders

Journal Article

Beiträge zur Algebra und Geometrie, ISSN 0138-4821, 10/2015, Volume 56, Issue 2, pp. 551 - 573

We study helix surfaces with parallel mean curvature vector in Euclidean space from a local point of view...

Geometry | 53C42 | Algebra | Convex and Discrete Geometry | Helix surfaces | Primary 53C40 | Algebraic Geometry | Mathematics | Parallel mean curvature vector

Geometry | 53C42 | Algebra | Convex and Discrete Geometry | Helix surfaces | Primary 53C40 | Algebraic Geometry | Mathematics | Parallel mean curvature vector

Journal Article

Acta crystallographica. Section A, Foundations of crystallography, ISSN 0108-7673, 01/2009, Volume 65, Issue 2, pp. 81 - 108

We present a method for geometric construction of periodic three‐dimensional Euclidean nets by projecting two...

triply periodic minimal surfaces | three‐dimensional Euclidean nets | kaleidoscopic hyperbolic tilings | two‐dimensional hyperbolic tilings | Triply periodic minimal surfaces | Kaleidoscopic hyperbolic tilings | Two-dimensional hyperbolic tilings | Three-dimensional Euclidean nets | Physical Sciences | Chemistry | Chemistry, Multidisciplinary | Crystallography | Science & Technology | Geometry | Euclidean space | Crystal structure

triply periodic minimal surfaces | three‐dimensional Euclidean nets | kaleidoscopic hyperbolic tilings | two‐dimensional hyperbolic tilings | Triply periodic minimal surfaces | Kaleidoscopic hyperbolic tilings | Two-dimensional hyperbolic tilings | Three-dimensional Euclidean nets | Physical Sciences | Chemistry | Chemistry, Multidisciplinary | Crystallography | Science & Technology | Geometry | Euclidean space | Crystal structure

Journal Article

Stochastic environmental research and risk assessment, ISSN 1436-3240, 9/2017, Volume 31, Issue 7, pp. 1583 - 1592

This paper addresses the problem of simulating multivariate random fields with stationary Gaussian increments in a d-dimensional Euclidean space...

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Intrinsic random fields | Fractional Brownian surfaces | Probability Theory and Stochastic Processes | Earth Sciences, general | Direct and cross variograms | Math. Appl. in Environmental Science | Computational Intelligence | Turning bands | Environment | Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution | Spectral density matrix | Self-similarity | Statistics & Probability | Engineering | Physical Sciences | Engineering, Environmental | Life Sciences & Biomedicine | Technology | Engineering, Civil | Water Resources | Environmental Sciences & Ecology | Mathematics | Science & Technology | Environmental Sciences | Analysis | Models | Algorithms | Euclidean geometry | Computer simulation | Simulation | Computer applications | Spectra | Euclidean space | Fields (mathematics) | Computing time

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Intrinsic random fields | Fractional Brownian surfaces | Probability Theory and Stochastic Processes | Earth Sciences, general | Direct and cross variograms | Math. Appl. in Environmental Science | Computational Intelligence | Turning bands | Environment | Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution | Spectral density matrix | Self-similarity | Statistics & Probability | Engineering | Physical Sciences | Engineering, Environmental | Life Sciences & Biomedicine | Technology | Engineering, Civil | Water Resources | Environmental Sciences & Ecology | Mathematics | Science & Technology | Environmental Sciences | Analysis | Models | Algorithms | Euclidean geometry | Computer simulation | Simulation | Computer applications | Spectra | Euclidean space | Fields (mathematics) | Computing time

Journal Article

Proteins, structure, function, and bioinformatics, ISSN 0887-3585, 10/2014, Volume 82, Issue 10, pp. 2585 - 2596

...‐reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs...

dimensionality reduction | isomap | protein conformation space | principal component analysis | free energy landscape | Dimensionality reduction | Protein conformation space | Free energy landscape | Isomap | Principal component analysis | Biochemistry & Molecular Biology | Biophysics | Life Sciences & Biomedicine | Science & Technology | Protein Structure, Secondary | Protein Unfolding | Bacterial Proteins - chemistry | Models, Molecular | Terminology as Topic | Statistics as Topic | Molecular Dynamics Simulation | Protein Folding | Peptide Fragments - chemistry | Surface Properties | Protein Conformation | Protein Interaction Domains and Motifs | Energy Transfer | Oligopeptides - chemistry | Principal Component Analysis | Proteins | Analysis | Index Medicus

dimensionality reduction | isomap | protein conformation space | principal component analysis | free energy landscape | Dimensionality reduction | Protein conformation space | Free energy landscape | Isomap | Principal component analysis | Biochemistry & Molecular Biology | Biophysics | Life Sciences & Biomedicine | Science & Technology | Protein Structure, Secondary | Protein Unfolding | Bacterial Proteins - chemistry | Models, Molecular | Terminology as Topic | Statistics as Topic | Molecular Dynamics Simulation | Protein Folding | Peptide Fragments - chemistry | Surface Properties | Protein Conformation | Protein Interaction Domains and Motifs | Energy Transfer | Oligopeptides - chemistry | Principal Component Analysis | Proteins | Analysis | Index Medicus

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 01/2017, Volume 306, pp. 958 - 972

Given a compact Riemannian manifold M without boundary, we show that large isoperimetric regions in M×Rk are tubular neighborhoods of M×{x}, with x∈Rk.

Symmetrization | Stable constant mean curvature surfaces | Riemannian cylinders | Isoperimetric inequality | Isoperimetric regions | Anisotropic scaling | Density estimates | Physical Sciences | Mathematics | Science & Technology

Symmetrization | Stable constant mean curvature surfaces | Riemannian cylinders | Isoperimetric inequality | Isoperimetric regions | Anisotropic scaling | Density estimates | Physical Sciences | Mathematics | Science & Technology

Journal Article

15.
Cartan for beginners

: differential geometry via moving frames and exterior differential systems

2016, Second edition., Graduate studies in mathematics, ISBN 1470409860, Volume 175., xviii, 453 pages

Book

Advances in mathematical physics, ISSN 1687-9120, 6/2016, Volume 2016, pp. 1 - 15

.... This Lie bracket will be employed to study integrability properties of evolution equations for null curves in a pseudo-Euclidean space...

Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Geometry | Commuting | Euclidean space | Operators | Brackets | Mathematical analysis | Evolution | Integral calculus | Fields (mathematics) | Recursion | Symmetry

Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Geometry | Commuting | Euclidean space | Operators | Brackets | Mathematical analysis | Evolution | Integral calculus | Fields (mathematics) | Recursion | Symmetry

Journal Article

2006, Mathematical surveys and monographs, ISBN 9780821840719, Volume 130, xiv, 260

Book

Annals of global analysis and geometry, ISSN 0232-704X, 10/2015, Volume 48, Issue 3, pp. 233 - 254

...Ann Glob Anal Geom (2015) 48:233–254
DOI 10.1007/s10455-015-9468-y
A connection between ﬂat fronts in hyperbolic space
and minimal surfaces in Euclidean space...

Geometry | 53C42 | Minimal surfaces | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Theoretical, Mathematical and Computational Physics | 53A35 | Mathematics | Group Theory and Generalizations | Flat fronts | Ribaucour transformations | Hyperbolic space | Physical Sciences | Science & Technology | Studies | Mathematical models | Euclidean space | Construction | Euclidean geometry | Transformations (mathematics) | Flats | Differential equations | Texts | Transformations

Geometry | 53C42 | Minimal surfaces | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Theoretical, Mathematical and Computational Physics | 53A35 | Mathematics | Group Theory and Generalizations | Flat fronts | Ribaucour transformations | Hyperbolic space | Physical Sciences | Science & Technology | Studies | Mathematical models | Euclidean space | Construction | Euclidean geometry | Transformations (mathematics) | Flats | Differential equations | Texts | Transformations

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 10/2018, Volume 41, Issue 4, pp. 1773 - 1793

We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C...

Minimal surfaces | 53B25 | Lorentz surfaces | Secondary 53A35 | Primary 53B30 | Mathematics, general | Mathematics | Pseudo-Euclidean space | Applications of Mathematics | General rotational surfaces | Parallel mean curvature vector | Physical Sciences | Science & Technology | Curvature | Euclidean geometry | Mathematics - Differential Geometry

Minimal surfaces | 53B25 | Lorentz surfaces | Secondary 53A35 | Primary 53B30 | Mathematics, general | Mathematics | Pseudo-Euclidean space | Applications of Mathematics | General rotational surfaces | Parallel mean curvature vector | Physical Sciences | Science & Technology | Curvature | Euclidean geometry | Mathematics - Differential Geometry

Journal Article

Central European journal of mathematics, ISSN 1895-1074, 10/2014, Volume 12, Issue 10, pp. 1586 - 1601

In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis...

hyperbolic or parabolic type | Topological Groups, Lie Groups | 53B25 | 53A35 | Probability Theory and Stochastic Processes | Mathematics | Lightlike mean curvature vector | Quasi-minimal surfaces | Rotational surfaces of elliptic | Geometry | Algebra | Mathematics, general | Number Theory | Pseudo-Euclidean 4-space with neutral metric | Physical Sciences | Science & Technology | Mathematics - Differential Geometry

hyperbolic or parabolic type | Topological Groups, Lie Groups | 53B25 | 53A35 | Probability Theory and Stochastic Processes | Mathematics | Lightlike mean curvature vector | Quasi-minimal surfaces | Rotational surfaces of elliptic | Geometry | Algebra | Mathematics, general | Number Theory | Pseudo-Euclidean 4-space with neutral metric | Physical Sciences | Science & Technology | Mathematics - Differential Geometry

Journal Article