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Show isometry of flow on a compact Riemannian manifold where the vector field is Killing

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#differential-geometry #riemannian-geometry #semi-riemannian-geometry
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1-form on the Riemannian manifold

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#riemannian-geometry
257
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Parallel translation via $e$-connection

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#differential-geometry #riemannian-geometry #information-theory #information-geometry
1.6k
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Isometry group of a compact manifold

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#differential-geometry #lie-groups #riemannian-geometry
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Geometrical interpretation of second fundamental form

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#differential-geometry #riemannian-geometry
182
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Integration of Laplacian of mean curvature on manifold.

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#riemannian-geometry #curvature #mean-curvature-flows
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Vanishing of curvature tensor implies path independence of parallel transport only to second order?

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#differential-geometry #riemannian-geometry #curvature #connections
336
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Focal set of a geodesic

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#differential-geometry #riemannian-geometry #smooth-manifolds #spherical-geometry #geodesic
15.2k
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Definition of gradient of a function $f$ in Riemannian manifold

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#definition #riemannian-geometry #semi-riemannian-geometry
516
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If a metric on $\Bbb R^n$ is flat, is the space globally isometric to Euclidean space?

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#differential-geometry #riemannian-geometry
371
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What is meant by "The Levi-Civita Connection is an $\mathfrak{so}(n)$-Valued 1-form"?

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#differential-geometry #riemannian-geometry #connections
517
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Covairant Derivative along the Constant Curve. What is the Mistake?

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#differential-geometry #riemannian-geometry
811
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Geodesics in rotating cylindrical coordinates: solving the coupled differential equations

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#riemannian-geometry
79
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How does one formalize the notions of cone points, etc..?

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#general-topology #differential-geometry #algebraic-topology #riemannian-geometry #geometric-topology
322
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Are nearby simple closed geodesics ambient isotopic?

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#general-topology #differential-geometry #riemannian-geometry #geodesic

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