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Existence of closed and intersecting geodesics on a compact manifold

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#differential-geometry #riemannian-geometry #classical-mechanics
80
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Riemann Tensor from Geodesic Deviation

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#geometry #differential-geometry #riemannian-geometry #curvature
1.8k
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The definition of Affine Invariant Riemannian Metric (AIRM)

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#matrices #riemannian-geometry
158
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Composition of a differential map and a smooth map

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#differential-geometry #riemannian-geometry #smooth-manifolds
272
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Problem on Do Carmo's definition of manifold

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#differential-geometry #manifolds #riemannian-geometry #smooth-manifolds
77
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Periodic motion on a torus and Lyusternik-Fet Theorem

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#differential-geometry #riemannian-geometry #calculus-of-variations #classical-mechanics
605
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Does dot product define a Riemannian metric on any smooth manifold?

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#differential-geometry #riemannian-geometry #smooth-manifolds
64
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How to derive the formal dual of the covariant exterior derivative?

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#geometry #differential-geometry #riemannian-geometry
54
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Riemaniann metric problem in K&N's book.

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#riemannian-geometry #inner-products
787
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Definition of a left-invariant vector field

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#differential-geometry #lie-groups #riemannian-geometry #smooth-manifolds
300
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To show that left invariant vector fields are completely determined by their values at a single point

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#proof-verification #lie-groups #riemannian-geometry #smooth-manifolds
546
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Any smooth vector field is a linear combination of left invariant vector fields

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#differential-geometry #lie-groups #riemannian-geometry #smooth-manifolds
119
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Surjective differentiable map is an isometry

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#differential-geometry #riemannian-geometry #hyperbolic-geometry #isometry
56
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Why $ (X(g_1), X(g_2),\cdots, X(g_n))=\operatorname{d}Y(X) $?

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#differential-geometry #riemannian-geometry
26
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Close points on a Lie Group with Left-Invariant Metric

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#lie-groups #riemannian-geometry

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