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An equation for Killing vector fields

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#differential-geometry #riemannian-geometry
193
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Why in the definition of a straight line we ask the tangential acceleration to be $0$ and not the normal acceleration to be $0$?

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#riemannian-geometry #intuition #geodesic
160
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If the lifts of two distinct geodesics have same end points at infinity, are the geodesics free homotopic?

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#differential-geometry #algebraic-topology #riemannian-geometry #covering-spaces #geodesic
144
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Riemannian compact six-dimensional manifolds Ricci-flat

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#differential-geometry #riemannian-geometry #curvature #general-relativity #string-theory
243
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What is the (oriented) orthonormal frame bundle of $(S^{3}\times S^{1})$?

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#group-theory #riemannian-geometry #fiber-bundles #principal-bundles
157
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Universal cover of a $3$-manifold is isometric to a cylinder

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#algebraic-topology #riemannian-geometry #smooth-manifolds #covering-spaces
109
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Surjectivity of the second fundamental form

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#differential-geometry #riemannian-geometry #connections #submanifold
60
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Length of a path does not depend of parametrizations

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#complex-analysis #differential-geometry #riemannian-geometry #hyperbolic-geometry
41
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Gauss curvature and 1st fundamental form

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#riemannian-geometry #curvature
2.6k
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Covariant Derivative of Basis Vectors

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#calculus #differential-geometry #riemannian-geometry #tensors #connections
162
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Different definitions of tensor fields

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#differential-geometry #riemannian-geometry #tensors #vector-fields
36
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Contraction of tensor by metric in mean curvature flow

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#riemannian-geometry #tensors #submanifold #mean-curvature-flows
44
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On 2d manifolds, is Ricci the only (intrinsic) symmetric 2-tensor which is derivative of metric up to 2nd order?

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#riemannian-geometry #curvature
167
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A question while pvoing existence bi-invariant Volume element on a compact and connected Lie group

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#differential-geometry #lie-groups #riemannian-geometry
309
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Smoothly extending a metric from a manifold with boundary to an attached cylinder

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#differential-geometry #manifolds #riemannian-geometry #smooth-manifolds #manifolds-with-boundary

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