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Notational Ambiguity: Covariant Derivative

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#differential-geometry #riemannian-geometry #differential-topology #laplacian #connections
89
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Coefficients of pullback connection

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#differential-geometry #riemannian-geometry
60
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Continuity of the closest point on a closed, but non-compact submanifold $S$ w.r.t. the point outside $S$ we measure the distance

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#real-analysis #analysis #differential-geometry #riemannian-geometry
22
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Length of rectifiable curves in Finsler spaces

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#metric-spaces #riemannian-geometry #arc-length #finsler-geometry
32
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Commutator formula between Hessian and Laplacian of a scalar function

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#differential-geometry #riemannian-geometry #index-notation
53
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Sign discrepancy between two different definitions of ricci curvature

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#differential-geometry #riemannian-geometry #curvature
39
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Hermitian metric as a section of the bundle $(E\otimes \bar{E})^*$

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#differential-geometry #riemannian-geometry
36
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Horizontal and vertical bundles of a linear space

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#linear-algebra #differential-geometry #riemannian-geometry #vector-bundles
97
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Relation between curvature form and the Riemann tensor

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#differential-geometry #riemannian-geometry #differential-forms #curvature #connections
24
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Two Neumann eigenfunctions with parallel gradients along the boundary of a manifold

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#partial-differential-equations #riemannian-geometry #smooth-manifolds #laplacian #elliptic-operators
59
Views

Why Morse Index Theorem imply Jacobi Theorem?

Published on
#riemannian-geometry
19
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Pointwise convergence of heat kernels on perturbed Riemannian manifolds

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#differential-geometry #riemannian-geometry #heat-equation #pointwise-convergence #parabolic-pde
48
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Vector field along a geodesic is Killing

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#differential-geometry #riemannian-geometry #general-relativity
44
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Isometric copy of the quotient $N$ embedded in the domain $M$ when $\pi:M\to N$ is a surjective Riemannian submersion?

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#geometry #differential-geometry #riemannian-geometry #geodesic
59
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Integrability of an open and convex subset $M$ of $\mathbb{R}^n$ with non-empty interior and compact closure (e.g. $(0,1)\times(0,1))$

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#integration #differential-geometry #riemannian-geometry #differential-forms #riemann-integration

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