List questions from manifolds

Published on 12 Apr 2026 - 9:18

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Compact cohomology group of connected n-dimensional connected oriented manifold

Published on 12 Apr 2026 - 22:41

598

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Definition of a cubic coordinate system

Published on 13 Apr 2026 - 12:35

249

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Prove: The boundary of the set $\{(x,y,z) \in \mathbb{R}^3 | z > \sqrt{x^2+y^2}\}$ isn't a smooth manifold.

Published on 16 Apr 2026 - 2:48

233

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Surjectivity of the exponential map on SO(2n)/U(n)

Published on 25 Mar 2026 - 22:03

636

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Pullback of the metric on $\mathbb S^n$ on $\mathbb R^n$.

Published on 03 May 2026 - 15:20

108

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Connectedness and dimension of a manifold

Published on 14 Apr 2026 - 4:57

43

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Calculate the area of $\partial G$ of $G = (z > x^2 + y^2$ and $x^2 + y^2 + z^2 < z)$ in $\mathbb{R}^3$.

Published on 16 Apr 2026 - 8:38

90

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Useful Formulas Analysis on Manifold

Published on 03 May 2026 - 15:20

1.4k

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Why $I = [0,1]$ is a $1$-manifold and $I^2$ not?

Published on 14 Apr 2026 - 23:06

348

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Bianchi identity proof : why we can consider $[X,Y]=[Y,Z]=[X,Z]=0$?

Published on 15 Apr 2026 - 9:07

70

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Is this map an immersion?

Published on 29 Apr 2026 - 2:26

52

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Question about connections and usual derivative.

Published on 03 May 2026 - 16:24

172

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If for each $\alpha, \beta$, the map $\psi_{\beta} \circ F \circ \phi_{\alpha}^{-1}$ is smooth, then $F$ is smooth.

Published on 17 Apr 2026 - 15:37

99

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number of roots on SO(3)

Published on 15 Apr 2026 - 10:03

List Question

Lagrangian Multipliers exercise

Compact cohomology group of connected n-dimensional connected oriented manifold

Definition of a cubic coordinate system

Prove: The boundary of the set $\{(x,y,z) \in \mathbb{R}^3 | z > \sqrt{x^2+y^2}\}$ isn't a smooth manifold.

Surjectivity of the exponential map on SO(2n)/U(n)

Pullback of the metric on $\mathbb S^n$ on $\mathbb R^n$.

Connectedness and dimension of a manifold

Calculate the area of $\partial G$ of $G = (z > x^2 + y^2$ and $x^2 + y^2 + z^2 < z)$ in $\mathbb{R}^3$.

Useful Formulas Analysis on Manifold

Why $I = [0,1]$ is a $1$-manifold and $I^2$ not?

Bianchi identity proof : why we can consider $[X,Y]=[Y,Z]=[X,Z]=0$?

Is this map an immersion?

Question about connections and usual derivative.

If for each $\alpha, \beta$, the map $\psi_{\beta} \circ F \circ \phi_{\alpha}^{-1}$ is smooth, then $F$ is smooth.

number of roots on SO(3)

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