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15
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Problem of connectdness with Orthonormal frame bundle O(M)

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#general-topology #differential-geometry #lie-groups #riemannian-geometry #principal-bundles
60
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Understanding of the definition of a Riemannian metric

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#differential-geometry #riemannian-geometry #curves #tangent-bundle
118
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Yano-Bochner integral formula.

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#differential-geometry #riemannian-geometry
845
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The idea of a bundle chart and bundle atlas.

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#differential-geometry #riemannian-geometry #intuition #vector-bundles #motivation
40
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Example of compact riemannian manifolds with seccional curvature negative

Published on
#riemannian-geometry #hyperbolic-geometry
88
Views

Isometry group of SO(n) and SE(n)

Published on
#differential-geometry #lie-groups #riemannian-geometry
280
Views

Haar measure of a Lie group is (locally) a Lebesgue measure times density?

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#differential-geometry #lie-groups #riemannian-geometry #smooth-manifolds #haar-measure
543
Views

Second fundamental form for Lie group $SO(n)$

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#differential-geometry #lie-groups #riemannian-geometry
55
Views

Induced Lie structure on the tanget space of a Lie group at the identity element.

Published on
#lie-groups #riemannian-geometry #lie-algebras
107
Views

Connected Einstein manifolds with dimension $\geq 3$

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#differential-geometry #riemannian-geometry #tensors
496
Views

Grassmannian is homogeneous, isotropic, and symmetric

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#differential-geometry #riemannian-geometry #grassmannian
288
Views

Isometry group of Riemannian symmetric spaces and Lie groups

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#differential-geometry #lie-groups #riemannian-geometry #lie-algebras #symmetric-spaces
86
Views

Product rule for matrices, think of them as vectors or not?

Published on
#riemannian-geometry
64
Views

$p:\widetilde{G} \rightarrow G$ a covering homomorphism, $\widetilde{H},H$ closed subgroups. Induced map on coset spaces is covering map.

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#differential-geometry #algebraic-topology #lie-groups #riemannian-geometry
821
Views

what does "patch" mean on manifold?

Published on
#geometry #manifolds #riemannian-geometry #polar-coordinates #noneuclidean-geometry

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