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The Riemann Curvature of The Round Sphere

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#linear-algebra #differential-geometry #riemannian-geometry #multilinear-algebra #connections
90
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A vector/tensor field is parallel if and only if its total covariant derivative vanishes

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#geometry #differential-geometry #riemannian-geometry #vector-fields
47
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Isometries of a submanifold with induced metric

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#riemannian-geometry #isometry #submanifold #semi-riemannian-geometry #pullback
76
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Question about the pullback of the Riemann metric via the exponential map.

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#differential-geometry #riemannian-geometry
80
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In proof of the Proposition 11.3. in the John Lee's Introduction to Riemannian manifolds

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#differential-geometry #riemannian-geometry
75
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What is the volume of the largest surface of revolution with constant positive curvature that can be embedded in the unit cube?

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#differential-geometry #optimization #riemannian-geometry #differential-topology #geometric-topology
113
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Why $\operatorname{tr}(\pi_r) = n-1$ ? ( Laplacian Comparison I, John Lee's Introduction to Riemannian manifolds )

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#differential-geometry #riemannian-geometry
51
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Help me solve this question if not atleast tell me What are the backgrounds needed to study to solve this question about Kenmotsu Manifold?

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#riemannian-geometry #smooth-manifolds #tensors #multilinear-algebra
67
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Taylor expansion on Riemannian manifolds

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#taylor-expansion #manifolds #riemannian-geometry #smooth-manifolds #curves
67
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Riemannian manifold, loop around two points and distance between these points

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#manifolds #riemannian-geometry
86
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Statistical invariants of Riemannian Manifolds

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#statistics #reference-request #metric-spaces #riemannian-geometry #geometric-measure-theory
60
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existence of a complete manifold with certain assumptions

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#differential-geometry #riemannian-geometry
39
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compact embeddings in manifolds

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#riemannian-geometry #sobolev-spaces
86
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Understanding Equality of Hausdorff Measures in Global and Submanifold Riemannian Metrics

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#real-analysis #measure-theory #riemannian-geometry #hausdorff-measure
45
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Square of a symmetric tensor on Riemannian manifold

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#differential-geometry #riemannian-geometry #tensors

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