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Vanish christoffel symbols implies $g_{ij,k}=0$

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#differential-geometry #riemannian-geometry
146
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Riemannian connection $ \lambda_{XX}=0$

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#riemannian-geometry
396
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Why the induced metric from the lie algebra of lie group $G$ is left invariant.

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#lie-groups #lie-algebras #riemannian-geometry
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Is exponential map locally a diffeomorphism w.r.t. base point?

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#differential-geometry #riemannian-geometry
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Distance function on complete Riemannian manifold.

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#manifolds #riemannian-geometry #geodesic
329
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Riemannian connection on Lie groups

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#differential-geometry #lie-groups #riemannian-geometry
74
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Example of nonuniqueness of asymptotes of a ray

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#differential-geometry #riemannian-geometry #examples-counterexamples
99
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existance of gradient conformal vector field on riemannian manifolds

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#riemannian-geometry
52
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Confused About Indices in Deriving Curvature

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#differential-geometry #riemannian-geometry #general-relativity
44
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About transformations of the metric: should we use the old or the new one to raise/lower indices?

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#differential-geometry #riemannian-geometry
387
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Flag Curvature in Finsler Geometry

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#riemannian-geometry
419
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how to define complete pseudo-riemannian manifold

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#riemannian-geometry
348
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Geodesic flow generated by Riemannian distance function

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#riemannian-geometry #symplectic-geometry
1.3k
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Why Differential Forms on Riemann surfaces?

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#abstract-algebra #complex-analysis #riemannian-geometry #riemann-surfaces
2k
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Why the differential of exponential map is the identity.

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#manifolds #riemannian-geometry

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