List questions from manifolds

Published on 30 Mar 2026 - 21:09

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What is the difference between Jacobian of maps between manifolds and matrix representation of its differential?

Published on 14 Jul 2019 - 15:59

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Let $v:\Bbb R \to \Bbb R^2$ be $C^{\infty}$. Then $\exists t_0\in (0,1)$ s.t $v(1)-v(0)$ is a scalar multiple of $\frac{dv}{dt}|_{t=t_0}$.

Published on 15 Jul 2019 - 0:15

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Derivation of a particular hopf fiber formula (pi rotation)

Published on 28 Mar 2026 - 2:56

91

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Gradient operator on Manifolds

Published on 30 Mar 2026 - 21:07

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Coordinate basis of tangent space

Published on 25 Mar 2026 - 12:53

255

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How do we prove that the double cone is not manifold?

Published on 16 Jul 2019 - 15:46

458

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Not understanding the definition of a differential of a map.

Published on 31 Mar 2026 - 21:56

62

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Should the set $\{ u \in C^\infty (M) : \int_M f e^u d\mu > 0 \}$ be convex?

Published on 17 Jul 2019 - 8:21

72

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Why does the smoothness of an induced map between manifolds depend on whether the image is a regular submanifold?

Published on 27 Mar 2026 - 3:41

57

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Volume of a k parallelopiped

Published on 17 Jul 2019 - 18:19

558

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Differential structure on regular submanifold vs. embedded submanifold

Published on 25 Mar 2026 - 9:05

44

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Is $TN$ a smooth embedded submanifold with or without boundary in $TM$?

Published on 26 Mar 2026 - 15:47

506

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Equivalent definitions for smooth embedding?

Published on 19 Jul 2019 - 9:08

992

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Are manifold subsets submanifolds?

Published on 31 Mar 2026 - 21:48

List Question

Gauss Lemma, Chapter 3 - Do Carmo's differential geometry.

What is the difference between Jacobian of maps between manifolds and matrix representation of its differential?

Let $v:\Bbb R \to \Bbb R^2$ be $C^{\infty}$. Then $\exists t_0\in (0,1)$ s.t $v(1)-v(0)$ is a scalar multiple of $\frac{dv}{dt}|_{t=t_0}$.

Derivation of a particular hopf fiber formula (pi rotation)

Gradient operator on Manifolds

Coordinate basis of tangent space

How do we prove that the double cone is not manifold?

Not understanding the definition of a differential of a map.

Should the set $\{ u \in C^\infty (M) : \int_M f e^u d\mu > 0 \}$ be convex?

Why does the smoothness of an induced map between manifolds depend on whether the image is a regular submanifold?

Volume of a k parallelopiped

Differential structure on regular submanifold vs. embedded submanifold

Is $TN$ a smooth embedded submanifold with or without boundary in $TM$?

Equivalent definitions for smooth embedding?

Are manifold subsets submanifolds?

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