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THE RIEMANNIAN MANIFOLD OF ALL RIEMANNIAN METRICS [PDF]
The Quarterly Journal of Mathematics, 1991 The space of all Riemannian metrics on a smooth second countable finite dimensional manifold is itself a smooth manifold modeled on the space of symmetric (0,2)-tensor fields with compact support. It carries a canonical Riemannian metric which is invariant under the action of the diffeomorphism group.
Olga Gil-Medrano, Peter W. Michor
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Dimensionality Reduction of SPD Data Based on Riemannian Manifold Tangent Spaces and Isometry [PDF]
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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On the curvatures of Riemannian manifolds [PDF]
Illinois Journal of Mathematics, 1966 J. A. Thorpe
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On decompositions of Riemannian manifolds [PDF]
Hiroshima Mathematical Journal, 1965 K. Miyashita
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On concurrent vector fields on Riemannian manifolds
AIMS Mathematics, 2023 It is shown that the presence of a non-zero concurrent vector field on a Riemannian manifold poses an obstruction to its topology as well as certain aspects of its geometry.
Amira Ishan
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Semi-Invariant Riemannian Submersions with Semi-Symmetric Non-Metric Connection
Journal of New Theory, 2021 In this paper, we investigate semi-invariant Riemannian submersion from a Kaehler manifold with semi-symmetric non-metric connection to a Riemannian manifold. We study the geometry of foliations with semi-symmetric non-metric connection.
Ramazan Sarı
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Generic Riemannian Maps from Nearly Kaehler Manifolds
Computer Sciences & Mathematics Forum, 2023 In order to generalise semi-invariant Riemannian maps, Sahin first introduced the idea of “Generic Riemannian maps”. We extend the idea of generic Riemannian maps to the case in which the total manifold is a nearly Kaehler manifold.
Richa Agarwal, Shahid Ali
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Qualar curvatures of pseudo Riemannian manifolds and pseudo Riemannian submanifolds
AIMS Mathematics, 2021 Some relations involving the qualar and null sectional curvatures for a pseudo Riemannian manifold are obtained. These curvatures are also investigated for pseudo-Riemannian submanifolds.
Mehmet Gülbahar
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Riemannian Hilbert Manifolds [PDF]
, 2017 In this article we collect results obtained by the authors jointly with other authors and we discuss old and new ideas. In particular we discuss singularities of the exponential map, completeness and homogeneity for Riemannian Hilbert quotient manifolds.
Francesco Mercuri, Leonardo Biliotti
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Simplexes in Riemannian manifolds [PDF]
Proceedings of the American Mathematical Society, 1993 Existence of a simplex with prescribed edge lengths in Euclidean, spherical, and hyperbolic spaces was studied recently. A simple sufficient condition of this existence is, roughly speaking, that the lengths do not differ too much. We extend these results to Riemannian n n -manifolds M n
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