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15
251
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Finite injectivity radius implies compactness

Published on
#riemannian-geometry #geodesic #higher-homotopy-groups
116
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Determining the projections onto the Horizontal and Vertical Space

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#linear-algebra #differential-geometry #riemannian-geometry #projection-matrices
415
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Intuition behind riemannian metric

Published on
#differential-geometry #riemannian-geometry #intuition #tensors
93
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Calibrator for unit speed curve

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#differential-geometry #riemannian-geometry #differential-forms #vector-fields #frenet-frame
256
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Conformal metrics

Published on
#differential-geometry #riemannian-geometry #riemann-surfaces
132
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An isometry between totally geodesic submanifolds is smooth?

Published on
#differential-geometry #riemannian-geometry #isometry
44
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Proving $\left(\mathbb{R}^2_+,\frac{1}{y}(dx^2+dy^2)\right)$ is not complete

Published on
#differential-geometry #riemannian-geometry #smooth-manifolds
178
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Reparameterized geodesics - proof

Published on
#differential-geometry #riemannian-geometry #geodesic
310
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Space of divergence-free vector fields on a Riemannian manifold

Published on
#riemannian-geometry #divergence-operator
366
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Detail in Perelman's proof of the Soul Conjecture: why $O(\delta^2)$ and not $O(\delta)$?

Published on
#differential-geometry #metric-spaces #riemannian-geometry #curvature
103
Views

Exhaustion in compact convex (totally geodesic) subsets of a complete manifold

Published on
#differential-geometry #convex-analysis #riemannian-geometry
256
Views

Existence of boundary cylindrical neighborhood for a compact manifold

Published on
#riemannian-geometry #manifolds-with-boundary #compact-manifolds
990
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Prove that the paraboloid in $R^3$, defined by $x^2 + y^2 - z^2 =a$ is a manifold if $a>0$. why does not $x^2 + y^2 -z^2 =0$ define a manifold?

Published on
#differential-geometry #differential-topology #riemannian-geometry #geometric-topology
314
Views

A symmetry of the Hodge star operator

Published on
#linear-algebra #differential-geometry #riemannian-geometry #inner-products #hodge-theory
59
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If I shift a curve in the normal direction, are its tangent vectors also shifted by parallel transport?

Published on
#riemannian-geometry #geodesic #submanifold

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