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Riemannian metric, PseudoRiemannian metric
, 1997
"... LANL xxx archive server Eprint No.: grqc/9802057 ..."
• Riemannian metrics • Connections
"... and curvature. Riemannian manifolds are smooth manifolds equipped with Riemannian metrics, which allow one to measure geometric quantities such as distance and angles and study geometric properties of curved space. This course covers core material that would be useful for many areas of mathematics a ..."
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and curvature. Riemannian manifolds are smooth manifolds equipped with Riemannian metrics, which allow one to measure geometric quantities such as distance and angles and study geometric properties of curved space. This course covers core material that would be useful for many areas of mathematics
The metric geometry of the manifold of Riemannian metrics
"... Abstract. We prove that the L 2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finitedimensional manifold induces a metric space structure. As the L 2 metric is a weak Riemannian metric, this fact does not follow from general results. In addition, we prove sev ..."
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Cited by 13 (3 self)
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Abstract. We prove that the L 2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finitedimensional manifold induces a metric space structure. As the L 2 metric is a weak Riemannian metric, this fact does not follow from general results. In addition, we prove
The Completion of the Manifold of Riemannian Metrics
"... Abstract. We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finitedimensional, orientable manifold with respect to a natural metric called the L 2 metric. The primary motivation for studying this problem comes from Teichmüller theory ..."
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Cited by 9 (5 self)
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Abstract. We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finitedimensional, orientable manifold with respect to a natural metric called the L 2 metric. The primary motivation for studying this problem comes from Teichmüller
Learning Riemannian Metrics
 In Proceedings of the 19th conference on Uncertainty in Artificial Intelligence (UAI
, 2003
"... We consider the problem of learning a Riemannian metric associated with a given differentiable manifold and a set of points. Our approach to the problem involves choosing a metric from a parametric family that is based on maximizing the inverse volume of a given dataset of points. From a stati ..."
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Cited by 17 (2 self)
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We consider the problem of learning a Riemannian metric associated with a given differentiable manifold and a set of points. Our approach to the problem involves choosing a metric from a parametric family that is based on maximizing the inverse volume of a given dataset of points. From a
On formal Riemannian metrics
"... Formal Riemannian metrics are characterized by the property that all products of harmonic forms are again harmonic. They have been studied over the last ten years and there are still many interesting open conjectures related to geometric formality. The existence of a formal metric implies Sullivan’s ..."
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Formal Riemannian metrics are characterized by the property that all products of harmonic forms are again harmonic. They have been studied over the last ten years and there are still many interesting open conjectures related to geometric formality. The existence of a formal metric implies Sullivan
Conformal deformation of a Riemannian metric to constant curvature
 J. Diff. Geome
, 1984
"... A wellknown open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe&apos ..."
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Cited by 308 (0 self)
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A wellknown open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe
Monotone Riemannian metrics and . . .
, 2008
"... We use the relative modular operator to define a generalized relative entropy for any convex operator function g on (0, ∞) satisfying g(1) = 0. We show that these convex operator functions can be partitioned into convex subsets each of which defines a unique symmetrized relative entropy, a unique f ..."
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family (parameterized by density matrices) of continuous monotone Riemannian metrics, a unique geodesic distance on the space of density matrices, and a unique monotone operator function satisfying certain symmetry and normalization conditions. We describe these objects explicitly in several important
On geodesic equivalence of Riemannian metrics and subRiemannian metrics on distributions of corank 1
, 2004
"... The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and subRiemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and subRiemannian cases in an unified way and obtain some algebraic necessary condi ..."
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The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and subRiemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and subRiemannian cases in an unified way and obtain some algebraic necessary
Results 1  10
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