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Springer Monographs in Mathematics, 2020
Valerii Berestovskii, Yurii Nikonorov
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Valerii Berestovskii, Yurii Nikonorov
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Ergodic Properties of Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature
, 2020Citation in format AMSBIB \Bibitem{Ano67} \by D.~V.~Anosov \paper Geodesic flows on closed Riemannian manifolds of negative curvature \serial Trudy Mat. Inst. Steklov. \yr 1967 \vol 90 \pages 3--210 \mathnet{http://mi.mathnet.ru/tm2795} \mathscinet{http:/
D. Anosov
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IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008
Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold.
Tong, Lin, Hongbin, Zha
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Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold.
Tong, Lin, Hongbin, Zha
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Simple Algorithms for Optimization on Riemannian Manifolds with Constraints
Applied Mathematics and Optimization, 2019We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces.
Changshuo Liu, Nicolas Boumal
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Gravitational magnetic curves on 3D Riemannian manifolds
International Journal of Geometric Methods in Modern Physics (IJGMMP), 2018In this paper, we study a special type of magnetic trajectories associated with a magnetic field [Formula: see text] defined on a 3D Riemannian manifold.
T. Körpınar, R. Demi̇rkol
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EQUIMORPHISMS OF RIEMANNIAN MANIFOLDS
Mathematics of the USSR-Izvestiya, 1972We establish a sufficient condition for stability of Riemannian manifolds, i.e. a property according to which every equimorphism of this manifold can be topologically extended to its absolute.
Efremovich, V. A. +2 more
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Symmetries on Riemannian Manifolds
Mathematische Nachrichten, 1988AbstractLocally symmetric KÄHLER manifolds may be characterized as almost HERMITian manifolds with symplectic or holomorphic local geodesic symmetries. We extend the notion of a local geodesic symmetry and in particular, give a similar characterization of all RIEMANNian locally s‐regular manifolds with an s‐structure of odd order.
Ledger, A. J., Vanhecke, L.
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Pseudocomplete Riemannian Analytic Manifolds
Mathematical Notes, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1993
Abstract Let M be a differentiable manifold. We say that M carries a pseudo Riemannian metric if there is a differentiable field g = (gm} , m ∈ M, of non-degenerate symmetric bilinear forms gm on the tangent spaces Mm of M. This makes the tangent space into an inner product space.
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Abstract Let M be a differentiable manifold. We say that M carries a pseudo Riemannian metric if there is a differentiable field g = (gm} , m ∈ M, of non-degenerate symmetric bilinear forms gm on the tangent spaces Mm of M. This makes the tangent space into an inner product space.
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