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$\exp_q^{-1}(\exp_p(tX)) = \exp_q^{-1}(p)+t\Gamma_{p\to q}(X)+O(t^2)$ as $t\to 0$?

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#differential-geometry #manifolds #differential-topology #riemannian-geometry #smooth-manifolds
102
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Is there any general theory about existence of smooth structures of a topological manifold?

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#geometry #differential-geometry #differential-topology #smooth-manifolds
637
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Definition of smooth maps between manifolds in $\mathbb{R}^n$

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#differential-topology #smooth-manifolds
208
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In a 2D Riemannian manifold, how does exponential map change the distances?

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#differential-geometry #manifolds #riemannian-geometry #smooth-manifolds
197
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Frenet Frame along a curve and Riemannian Curvature on $S^2$

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#differential-geometry #riemannian-geometry #smooth-manifolds #curves #frenet-frame
401
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Orientation of a Manifold with Trivial Tangential Bundle

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#smooth-manifolds #orientation #tangent-bundle
135
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Reduced bundles and global sections of associated bundle

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#differential-geometry #smooth-manifolds #principal-bundles
824
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Can a diffeomorphism not be an immersion or a submersion

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#differential-geometry #smooth-manifolds
233
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An example of a two dimensional integrable distribution on $SO(3)$

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#differential-geometry #smooth-manifolds
103
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Understanding submersions in differential topology

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#multivariable-calculus #differential-geometry #differential-topology #smooth-manifolds
51
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Submersions in differential topology

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#multivariable-calculus #differential-geometry #differential-topology #smooth-manifolds
92
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Question about a proposition in Kobayashi book about $G$-structures.

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#differential-geometry #manifolds #smooth-manifolds #fiber-bundles #principal-bundles
506
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Doubt in the definition of principal bundle.

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#differential-geometry #lie-groups #smooth-manifolds #fiber-bundles #principal-bundles
313
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$1$-parameter group terminology problem.

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#manifolds #lie-groups #lie-algebras #smooth-manifolds #vector-fields
324
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Smooth Manifolds: Charts or Parametrizations?

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#general-topology #manifolds #differential-topology #smooth-manifolds

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