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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.
È A Loginov+2 more
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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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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.
Lieven Vanhecke, Aj Ledger
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2018
Abstract This chapter is about Riemannian manifolds. It first discusses the metric manifold and the Levi-Civita connection, determining if the metric is Riemannian or Lorentzian. Next, the chapter turns to the properties of the curvature tensor.
Nathalie Deruelle, Jean-Philippe Uzan
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Abstract This chapter is about Riemannian manifolds. It first discusses the metric manifold and the Levi-Civita connection, determining if the metric is Riemannian or Lorentzian. Next, the chapter turns to the properties of the curvature tensor.
Nathalie Deruelle, Jean-Philippe Uzan
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Riemannian Metrics and Riemannian Manifolds
2020Fortunately, the rich theory of vector spaces endowed with a Euclidean inner product can, to a great extent, be lifted to the tangent bundle of a manifold. The idea is to equip the tangent space TpM at p to the manifold M with an inner product 〈−, −〉p, in such a way that these inner products vary smoothly as p varies on M. It is then possible to define
Jean Gallier, Jocelyn Quaintance
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The Manifolds Covered by a Riemannian Homogeneous Manifold
American Journal of Mathematics, 1960Introduction. The sphere is known to be the universal covering for complete connected Riemannian manifolds of constant positive curvature. More precisely, if M is an n-dimensional complete connected Riemannian manifold of constant sectional curvature k2 > 0 with k > 0, and if Sn is the sphere of radius k-1 in Euclidean space RI'+', with the induced ...
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The Fibring of Riemannian Manifolds [PDF]
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