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Doubt in the proof of Poincaire's theorem using Gauss-Bonnet theorem (local).

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#differential-geometry #riemannian-geometry #proof-explanation #curvature #triangulation
235
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Complete Kähler Metrics

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#differential-geometry #riemannian-geometry
91
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Each connected component lies in a hemisphere

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#manifolds #riemannian-geometry #smooth-manifolds #projective-space #spherical-geometry
282
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Is the integral of the curvature the variation of the parallel transport even if there are corners on the on the border of the region?

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#differential-geometry #riemannian-geometry #curvature
2.5k
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How does a metric tensor describe geometry on a manifold?

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#differential-geometry #metric-spaces #riemannian-geometry
1k
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Tangent spaces and local approximations of manifolds

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#differential-geometry #riemannian-geometry
458
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Angle between points in hyperbolic space

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#geometry #metric-spaces #riemannian-geometry #hyperbolic-geometry
397
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Completion of a riemannian manifold.

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#metric-spaces #riemannian-geometry
1k
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If $S$ is homeomorphic to a torus $\Rightarrow$ $S$ has a differentiable vector field without singular points

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#differential-geometry #riemannian-geometry #smooth-manifolds #surfaces #vector-fields
298
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bound on covariant derivative of second fundemantal form

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#differential-geometry #riemannian-geometry #minimal-surfaces
194
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Simons '68 minimal varieties notation

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#differential-geometry #riemannian-geometry #minimal-surfaces
886
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Sobolev spaces on Riemannian manifold and the Laplacian

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#differential-geometry #riemannian-geometry #sobolev-spaces #laplacian
137
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Focal points of Clifford torus

Published on
#riemannian-geometry
287
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Tangent space of hyperboloid

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#differential-geometry #riemannian-geometry
60
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Horoballs based at the same point in Hadamard manifolds

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#geometry #differential-geometry #metric-spaces #riemannian-geometry

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