Results 1 to 10 of about 3,318 (168)
A universal Riemannian foliated space
Topology and Its Applications, 2016 It is proved that the isometry classes of pointed connected complete Riemannian n-manifolds form a Polish space with the topology described by the C∞ convergence of manifolds. This space has a canonical partition into sets defined by varying the distinguished point into each manifold.
Jesus A Alvarez Lopez, Ramon Barral Lijo
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On hypersurfaces of Lorentzian standard 4-space forms satisfying a biconservativity condition [PDF]
Journal of Mahani Mathematical Research, 2023 In this manuscript, we consider an extended version of biconservativity condition (namely, ${\textrm C}$-biconservativity) on the Riemannian hypersurfaces of Lorentzian standard 4-space forms.
Firooz Pashaie
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On the Geometry of Three-dimensional Pseudo-Riemannian Homogeneous Spaces. I [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 The problem of establishing links between the curvature and the topological structure of a manifold is one of the important problems of geometry. In general, the purpose of the research of manifolds of various types is rather complicated.
Natal’ya Pavlovna Mozhey
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Mathematics, 2022 In shape analysis, the interpolation of shapes’ trajectories is often performed by means of geodesics in an appropriate Riemannian Shape Space. Over the past several decades, different metrics and shape spaces have been proposed, including Kendall shape ...
Valerio Varano +5 more
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Barycentric interpolation on Riemannian and semi-Riemannian spaces [PDF]
Monthly Notices of the Royal Astronomical Society, 2019 ABSTRACT Interpolation of data represented in curvilinear coordinates and possibly having some non-trivial, typically Riemannian or semi-Riemannian geometry is a ubiquitous task in all of physics. In this work, we present a covariant generalization of the barycentric coordinates and the barycentric interpolation method for Riemannian and
Pauli Pihajoki +2 more
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On the Geometry of Three-dimensional Pseudo-Riemannian Homogeneous Spaces. II [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 The problem of establishing links between the curvature and the topological structure of a manifold is one of the important problems of the geometry. In general, the purpose of the research of manifolds of various types is rather complicated.
Mozhey, Natal’ya Pavlovna
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Dimensionality Reduction of SPD Data Based on Riemannian Manifold Tangent Spaces and Isometry
Entropy, 2021 Symmetric positive definite (SPD) data have become a hot topic in machine learning. Instead of a linear Euclidean space, SPD data generally lie on a nonlinear Riemannian manifold.
Wenxu Gao +3 more
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Geometric Inequalities for a Submanifold Equipped with Distributions
Mathematics, 2022 The article introduces invariants of a Riemannian manifold related to the mutual curvature of several pairwise orthogonal subspaces of a tangent bundle. In the case of one-dimensional subspaces, this curvature is equal to half the scalar curvature of the
Vladimir Rovenski
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Subspaces Of Riemannian Spaces [PDF]
Canadian Journal of Mathematics, 1955 In this paper, results obtained by the author for Riemannian Spaces Vn imbedded in Euclidean Spaces EN (3; 4) are extended to Vn imbedded in VN.The first section is introductory. In §2 the general result is obtained. This is the establishment of a certain dependency among the three basic sets of equations of the Vn with respect to the VN, namely the ...
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The Geometry of Riemannian Spaces [PDF]
Transactions of the American Mathematical Society, 1934 The primary purpose of this paper is to expose, in as simple and clear a form as is possible, the fundamentals of the geometric structure of a Riemannian space. It is a general truth that the methods which pierce most deeply into the heart of a geometric theory are invariant methods, that is, methods which are independent of the choice of the ...
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