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Harmonic map and pullback metric

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#differential-geometry #reference-request #riemannian-geometry #harmonic-functions
299
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Left multiplication isometry?

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#abstract-algebra #group-theory #lie-groups #riemannian-geometry #lie-algebras
2.7k
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Parallel Translation is Path Independent iff Manifold is Flat

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#differential-geometry #riemannian-geometry
466
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This map is an isometry (in the Riemannian sense) of the hyperbolic plane. Why is the following a proof of it?

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#geometry #riemannian-geometry #hyperbolic-geometry
2.2k
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Understanding the first fundamental form of a surface, how the parametrization doesn't matter.

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#differential-geometry #riemannian-geometry #surfaces #differential-forms
141
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Harmonic map into $S^n \times \mathbb{R}$

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#differential-geometry #reference-request #riemannian-geometry #harmonic-functions
50
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Why is $\nabla_X (\varphi Y)=\nabla_X(0\cdot\varphi Y)$?

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#differential-geometry #riemannian-geometry #proof-explanation
168
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Hessian of the Stereographic projection

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#differential-geometry #reference-request #riemannian-geometry
939
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Christoffel symbols of $S^n$ in polar coordinates

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#differential-geometry #reference-request #riemannian-geometry
204
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Finding a domain of an integral curve of a vector field

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#riemannian-geometry #smooth-manifolds #vector-fields #morse-theory
127
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A step in proof of Bishop-Gromov Theorem

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#differential-geometry #riemannian-geometry
111
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Is any smooth deformation of a metric in dimension 1 conformal?

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#differential-geometry #riemannian-geometry #conformal-geometry
306
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lower bound on volume of balls

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#differential-geometry #riemannian-geometry
214
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Physical meaning of Hawking's Singularity theorem

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#riemannian-geometry #mathematical-physics #geodesic #general-relativity #semi-riemannian-geometry
372
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Polynomial in the components of the curvature tensor

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#differential-geometry #polynomials #riemannian-geometry #heat-equation #laplacian

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