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Injectivity of the Differential of Smooth Map

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#differential-geometry #manifolds #riemannian-geometry
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Nonexistence of local isometry between equidimensional Riemannian manifolds

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#differential-geometry #riemannian-geometry #inner-products #isometry
577
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Connection between harmonic functions, Bochner Laplacian and Ricci curvature

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#differential-geometry #riemannian-geometry
140
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Natural derivative of Vector Fields on manifolds

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#differential-geometry #riemannian-geometry
945
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second fundamental form and connection forms

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#differential-geometry #riemannian-geometry
392
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Can a volume form on a submanifold be extended to a parallel form in a neighbourhood?

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#differential-geometry #riemannian-geometry #differential-forms
617
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Calculating euler characteristic and geodesic curvature

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#differential-geometry #riemannian-geometry #curvature
2k
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Intuition behind eigenfunctions of the Laplacian operator

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#differential-geometry #partial-differential-equations #riemannian-geometry #spectral-theory #laplacian
2.3k
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Why is a diffeomorphism an isometry if and only if it commutes with the Laplacian?

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#riemannian-geometry #laplacian
79
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Can the Lie group structure be recovered from the geometry of an invariant metric?

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#lie-groups #riemannian-geometry
1k
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Definition of covering (deck) transformation for smooth manifolds: Are they diffeomorphisms?

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#differential-geometry #algebraic-topology #riemannian-geometry #covering-spaces
247
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If M is compact and N is connected, then locally isometry is symmetric?

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#riemannian-geometry
256
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Jacobi field strange condition.

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#real-analysis #analysis #differential-geometry #manifolds #riemannian-geometry
2.3k
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Local existence of parallel vector field

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#geometry #differential-geometry #riemannian-geometry
566
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Covariant and partial derivative commute?

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#real-analysis #analysis #differential-geometry #differential-topology #riemannian-geometry

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