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Question about Unit tangent bundle of embedded submanifold $M$ in $T\mathbb{R}^{m}$

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#smooth-manifolds #tangent-bundle #submanifold
2.3k
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What is the mean curvature of an infinitely long cylinder?

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#differential-geometry #curvature #submanifold
131
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Fixing orientation of connected smooth manifold in $\mathbb{R}^n$ by a single chart

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#smooth-manifolds #orientation #submanifold
246
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The structure of the embedded submanifold.

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#manifolds #examples-counterexamples #submanifold
146
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Is a surface curve made of planar points necessarily a line?

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#differential-geometry #riemannian-geometry #surfaces #curves #submanifold
51
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A cylinder is not stable for area under a volume constraint

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#differential-geometry #surfaces #calculus-of-variations #submanifold
288
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Why cone of revolution is not a submanifold?

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#differential-geometry #manifolds #submanifold
199
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The asymptotic set of the second fundamental form of a hypersurface

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#linear-algebra #differential-geometry #vector-spaces #riemannian-geometry #submanifold
50
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Boundary and interior of perturbed manifold

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#differential-geometry #differential-topology #smooth-manifolds #manifolds-with-boundary #submanifold
89
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Pushforward of a chart

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#differential-geometry #smooth-manifolds #manifolds-with-boundary #submanifold #pushforward
31
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If $ϕ$ is a boundary chart of a $k$-dimensional submanifold $M$ with boundary, then $(T_xϕ)v\in\mathbb R^{k-1}×\{0\}$ for all $v\in T_x\:\partial M$

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#differential-geometry #manifolds-with-boundary #tangent-spaces #submanifold #pushforward
165
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A tangent vector of a manifold $M$ with boundary is either inward/outward pointing or tangential to $\partial M$

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#differential-geometry #manifolds-with-boundary #tangent-spaces #submanifold #pushforward
54
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Prove that $S$ is submanifold of $\mathbb{R}^4$

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#differential-geometry #smooth-manifolds #submanifold
223
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Does the identity map have injective differential?

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#differential-geometry #submanifold
46
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Which space is $L^1(\partial\Omega)$?

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#lp-spaces #sobolev-spaces #manifolds-with-boundary #submanifold #trace-map

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