List questions from manifolds

Published on 03 Apr 2026 - 6:05

82

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Show that $\{\theta_i\}$ is a differentiable partition of unity, then $\sum i\theta_i$ is a proper map

Published on 04 Apr 2026 - 11:30

136

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Prove $g(t,u)$ is a regular surface when it may have singular points.

Published on 29 Mar 2026 - 8:17

136

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How to prove that the set of matrices of rank not greater than r is a smooth manifold?

Published on 04 Apr 2026 - 11:28

45

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How to show $\theta: H\times N\to N$ defined by $\theta(h,n)=hnh^{-1}$ is smooth?

Published on 03 Apr 2026 - 6:07

39

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$\omega=df$ with $\omega$ compact supported: $f$ compact supported possible?

Published on 08 Oct 2019 - 8:58

291

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Show that submanifolds are in fact manifolds.

Published on 04 Apr 2026 - 11:29

473

Views

Restriction of a map between manifolds is smooth?

Published on 27 Mar 2026 - 5:40

270

Views

How to show there exists a smooth local frame $(\tilde{X_1},\cdots,\tilde{X_n})$ on some neighborhood of $A$ such that $\tilde{X_i}|_A=X_i$?

Published on 28 Mar 2026 - 14:39

76

Views

Yamabe problem but for Ricci curvature instead: what do we know?

Published on 27 Mar 2026 - 6:59

52

Views

Lie's 3rd theorem

Published on 31 Mar 2026 - 23:25

144

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Immersion of non-orientable surface in $\mathbb R^3$ with conditions on the height function

Published on 28 Mar 2026 - 3:55

84

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Quotient topology - Tu's Introduction to manifolds

Published on 11 Oct 2019 - 9:52

93

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Connection on principle bundle

Published on 31 Mar 2026 - 23:26

1.2k

Views

Explicit description of tangent spaces of $O(n)$

Published on 03 Apr 2026 - 6:06

List Question

Can the closedness condition for $H$ be removed?

Show that $\{\theta_i\}$ is a differentiable partition of unity, then $\sum i\theta_i$ is a proper map

Prove $g(t,u)$ is a regular surface when it may have singular points.

How to prove that the set of matrices of rank not greater than r is a smooth manifold?

How to show $\theta: H\times N\to N$ defined by $\theta(h,n)=hnh^{-1}$ is smooth?

$\omega=df$ with $\omega$ compact supported: $f$ compact supported possible?

Show that submanifolds are in fact manifolds.

Restriction of a map between manifolds is smooth?

How to show there exists a smooth local frame $(\tilde{X_1},\cdots,\tilde{X_n})$ on some neighborhood of $A$ such that $\tilde{X_i}|_A=X_i$?

Yamabe problem but for Ricci curvature instead: what do we know?

Lie's 3rd theorem

Immersion of non-orientable surface in $\mathbb R^3$ with conditions on the height function

Quotient topology - Tu's Introduction to manifolds

Connection on principle bundle

Explicit description of tangent spaces of $O(n)$

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