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Uniqueness of bi-invariant metrics on Lie groups?

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#lie-groups #riemannian-geometry
1.5k
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use of existence of bi-invariant differential form on a Lie group?

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#lie-groups #riemannian-geometry
55
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Show that the section $g(x_1,x_2,x_3)=x_1^2dx_1^2+dx_2^2+dx_3^2$ defines a Riemannian metric on $\mathbb{R}^3 - \{x_1=0\}$

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#differential-geometry #riemannian-geometry
214
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(Co)Tangent bundle of Cone manifold

Published on
#riemannian-geometry #differential-forms #vector-bundles
730
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Divergence of a tensor with respect to the Levi-Civita connection

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#differential-geometry #riemannian-geometry #curvature
396
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Mean Curvature Flow

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#differential-geometry #riemannian-geometry #mean-curvature-flows
906
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Is the shortest path in flat hyperbolic space straight relative to Euclidean space?

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#differential-geometry #riemannian-geometry #hyperbolic-geometry #euler-lagrange-equation #semi-riemannian-geometry
400
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Is it mathematically correct to say that if the metric is flat/curved the *shortest* path is/not a Euclidean straight line?

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#geometry #differential-geometry #metric-spaces #riemannian-geometry #euler-lagrange-equation
620
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Geodesic Flow is an Anosov Flow

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#dynamical-systems #riemannian-geometry
151
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Geodesic flow on a compact manifold is defined for all time

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#dynamical-systems #riemannian-geometry
1.7k
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Why the flat torus cannot be immersed in euclidean plane?

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#riemannian-geometry #riemann-surfaces
1.3k
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parallel vector field

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#real-analysis #analysis #differential-geometry #manifolds #riemannian-geometry
101
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Doubts about a proof by Petersen regarding totally convex sets

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#proof-verification #riemannian-geometry
469
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Normal coordinate parallel along radial geodesics?

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#real-analysis #differential-geometry #manifolds #riemannian-geometry
676
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Unique metric for the Hyperbolic Half Plane Model?

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#reference-request #lie-groups #riemannian-geometry

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