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15
61
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Basic Lie group Theory

Published on
#group-theory #lie-groups #smooth-manifolds #topological-groups
68
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Proof that two charts on the tangent bundle $TM$ are $C^\infty(M)$-compatible

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#differential-geometry #smooth-manifolds #smooth-functions #tangent-bundle
88
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Local diffeomorphism between a disk and a sphere

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#smooth-manifolds #surfaces #smooth-functions #diffeomorphism
341
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Christoffel symbols, dual space

Published on
#differential-geometry #smooth-manifolds #connections
369
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When do (pointwise) non-zero differential forms have non-zero de Rham cohomology?

Published on
#differential-topology #smooth-manifolds #de-rham-cohomology
372
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Why $x$ has superscript $i$ in the expression $\partial/\partial x^i$ (Differential Geometry)?

Published on
#differential-geometry #notation #smooth-manifolds #tensors
175
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Construct interior chart of a manifold boundary $\partial M$ from a boundary chart of the manifold $M$

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#differential-geometry #manifolds #smooth-manifolds #manifolds-with-boundary #submanifold
200
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Equivariant rank theorem.

Published on
#smooth-manifolds #group-actions #equivariant-maps
102
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Show an identity for the Laplace-Beltrami operator

Published on
#differential-geometry #smooth-manifolds #laplacian #manifolds-with-boundary #tangent-spaces
56
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Is the inverse of an interior chart of a submanifold an immersion?

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#differential-geometry #smooth-manifolds #frechet-derivative #diffeomorphism #submanifold
369
Views

Is Gauss map a diffeomorphism onto its image in this case?

Published on
#riemannian-geometry #smooth-manifolds #surfaces #curvature #diffeomorphism
322
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Alternate definition for differential form on smooth manifold

Published on
#differential-geometry #manifolds #smooth-manifolds #differential-forms
115
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Show this identity for the surface measure on the boundary of a submanifold

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#differential-geometry #smooth-manifolds #geometric-measure-theory #manifolds-with-boundary #submanifold
81
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The Euclidean metric after the mapping $f:\Bbb R^2 \to \Bbb R^{2+}$ with $f(x,y)=(e^x,e^y),$ is what?

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#differential-geometry #metric-spaces #manifolds #euclidean-geometry #smooth-manifolds
218
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Find a specific countable atlas for a smooth submanifold with boundary

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#differential-geometry #smooth-manifolds #manifolds-with-boundary #submanifold

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