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15
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Intrinsic proof that sprays induce involutions

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#differential-geometry #riemannian-geometry #connections #lie-derivative #tangent-bundle
69
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Is the derivative of a path on a manifold always on the tangent space?

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#geometry #manifolds #riemannian-geometry #smooth-manifolds
25
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What changes in the 1st and 2nd variation formulas and the information contained in the index form for a Lorentzian instead of a riemannian manifold?

Published on
#differential-geometry #riemannian-geometry #semi-riemannian-geometry
42
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What information does the sign of the index form gives me about the geodesic?

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#differential-geometry #riemannian-geometry #geodesic
69
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Smooth Riemannian metric is locally real analytic?

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#differential-geometry #riemannian-geometry #analytic-functions #analyticity
42
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How does the riemann tensor symplify to normal components in the second variation formula?

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#differential-geometry #riemannian-geometry #smooth-manifolds #tensors #curvature
87
Views

Verify that surfaces are isometric by looking at pullback of Levi-Civita connection

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#differential-geometry #riemannian-geometry
41
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Understanding final statement of the Cheng's Maximal Diameter Theorem ( John Lee's Introduction to Riemannian manifolds )

Published on
#riemannian-geometry
33
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Mixing metric tensors on Riemannian manifold

Published on
#metric-spaces #riemannian-geometry
54
Views

Contraction of the determinant

Published on
#differential-geometry #riemannian-geometry #determinant #tensors #exterior-algebra
27
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Are sufficiently small closed geodesic balls compact?

Published on
#riemannian-geometry #compactness #geodesic
62
Views

Why $S_{\gamma'(0)}(J(0))=0$ for the geodesic sub-manifold?

Published on
#riemannian-geometry
52
Views

Cut-off function with good property

Published on
#real-analysis #analysis #differential-geometry #riemannian-geometry
115
Views

Is there a complete list of all compact spaces covered by $\mathbb{R}^2$?

Published on
#algebraic-topology #manifolds #riemannian-geometry #covering-spaces
36
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inequality equivalence in tangent spaces and $\mathbb{R}^N$

Published on
#differential-geometry #riemannian-geometry

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