Results 1 to 10 of about 1,165 (155)
Spherical Ruled Surfaces in S3 Characterized by the Spherical Gauss Map [PDF]
Mathematics, 2020 The Laplace operator on a Riemannian manifold plays an important role with eigenvalue problems and the spectral theory. Extending such an eigenvalue problem of smooth maps including the Gauss map, the notion of finite-type was introduced.
Young Ho Kim, Sun Mi Jung
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Pseudo-Spherical Submanifolds with 1-Type Pseudo-Spherical Gauss Map [PDF]
Results in Mathematics, 2016 In this work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere $\mathbb{S}^4_s(1)$ with index s, $s=1, 2$, and having harmonic pseudo-spherical Gauss map.
Bektaş, Burcu +2 more
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On spherical submanifolds with finite type spherical Gauss map [PDF]
Advances in Geometry, 2016 Abstract Chen and Lue (2007) initiated the study of spherical submanifolds with finite type spherical Gauss map. In this paper, we firstly prove that a submanifold Mn of the unit sphere Sm−1 has non-mass-symmetric 1-type spherical Gauss map if and only if Mn is an open part of a small n-sphere of a totally geodesic (n + 1)- sphere Sn+1 .
Bektaş, Burcu, Dursun, Uğur
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SPHERICAL SUBMANIFOLDS WITH FINITE TYPE SPHERICAL GAUSS MAP [PDF]
Journal of the Korean Mathematical Society, 2007 The study of Euclidean submanifolds with finite type “classical” Gauss map was initiated by B.-Y. Chen and P. Piccinni in [11]. On the other hand, it was believed that for spherical submanifolds the concept of spherical Gauss map is more relevant than the classical one (see [20]).
Bang-Yen Chen, Huei-Shyong Lue
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Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map [PDF]
Annals of Global Analysis and Geometry, 2017 We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification is obtained, while in other cases the solutions are described by an explicit system of partial differential ...
Bektas, Burcu +2 more
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Classification of surfaces in a pseudo‐sphere with 2‐type pseudo‐spherical Gauss map
Mathematische Nachrichten, 2017 AbstractIn this article, we study submanifolds in a pseudo‐sphere with 2‐type pseudo‐spherical Gauss map. We give a characterization theorem for Lorentzian surfaces in the pseudo‐sphere with zero mean curvature vector in and 2‐type pseudo‐spherical Gauss map.
Bektaş, Burcu +2 more
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The Gauss map of a hypersurface in Euclidean sphere and the spherical Legendrian duality
Topology and its Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Spheres and Tori as Elliptic Linear Weingarten Surfaces
Mathematics, 2022 The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric.
Dong-Soo Kim, Young Ho Kim, Jinhua Qian
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Continuous Maps from Spheres Converging to Boundaries of Convex Hulls
Forum of Mathematics, Sigma, 2021 Given n distinct points $\mathbf {x}_1, \ldots , \mathbf {x}_n$ in $\mathbb {R}^d$ , let K denote their convex hull, which we assume to be d-dimensional, and $B = \partial K $ its $(d-1)$ -dimensional boundary.
Joseph Malkoun, Peter J. Olver
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Hypersurfaces of the spherical type degenerated
Selecciones Matemáticas, 2020 In this work, we define the hypersurfaces of the spherical type degenerated (in short DST-hypersurfaces), these hypersurfaces has the geometric property that the middle spheres pass through the origin of the Euclidean space.
Armando M. V. Corro +2 more
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