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Two definitions of covariant derivatives in the setting of surfaces in $\mathbb{R}^3$

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#differential-geometry #riemannian-geometry
78
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Questions about definitions in Surface Theory

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#differential-geometry #manifolds #riemannian-geometry #surfaces #riemann-surfaces
475
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What is the meaning and importance of the Hodge codiferential?

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#differential-geometry #manifolds #riemannian-geometry #mathematical-physics #hodge-theory
148
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Is a rotationally invariant surface necessarily invariant w.r.t. reflection?

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#differential-geometry #riemannian-geometry #surfaces #isometry
1.5k
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Computing the index of a singular point of a vector field

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#riemannian-geometry #vector-analysis
159
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For any open set $U$ in $M$ and a point $p∈U$, there is a coordinate open set $U_α$ such that $p∈U_α⊂U.$

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#differential-geometry #manifolds #riemannian-geometry #smooth-manifolds
265
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The restriction of a Riemannian metric might be degenerate?

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#geometry #differential-geometry #riemannian-geometry
188
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Decomposing symmetric tensor field into sum of metric and tensor product

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#linear-algebra #differential-geometry #riemannian-geometry
659
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Uniformization of metrics vs. uniformization of Riemann surfaces

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#differential-geometry #riemannian-geometry #riemann-surfaces #riemann-sphere
32
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How can I prove that being the functions $g_{ij}$ from the class $C^r$ on $U$ is independent on choosing the local coordinate system ???

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#differential-geometry #manifolds #riemannian-geometry
76
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Extending a vector field to a ball

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#manifolds #riemannian-geometry #smooth-manifolds #vector-fields #connections
112
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Conservation laws for geometric/gravitational functionals

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#differential-geometry #riemannian-geometry #physics #mathematical-physics
173
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If $H/\Gamma$ is a compact Riemann surface , the generator of $\Gamma$ is not commutative

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#riemannian-geometry #riemann-surfaces
641
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Umbilic points and ellipsoid

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#geometry #differential-geometry #riemannian-geometry
1.6k
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Existence and Uniqueness of Geodesics

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#differential-geometry #manifolds #riemannian-geometry #smooth-manifolds

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