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Geodesic Convexity of the Symmetric Eigenvalue Problem and Convergence of Steepest Descent. [PDF]
J Optim Theory ApplAlimisis F, Vandereycken B.
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Meta‐Golden Riemannian manifolds
Mathematical Methods in the Applied Sciences, 2022The logarithmic spiral in nature has been given as an example of the golden ratio until now. But recently, it has been shown that this is not true, and the logarithmic spiral has actually been shown to provide the so‐called Meta‐Golden‐Chi ratio. Inspiring from Meta‐Golden‐Chi ratio, we introduce almost Meta‐Golden manifolds, give a characterization ...
Fulya Şahin, Bayram Şahin
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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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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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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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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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