List questions from tangent-spaces

69

Views

Is the matrix $dF_p$ invertible when $F=(y^1, \dots, y^n)$ and $(dy^1\big|_p,\dots, dy^n\big|_p)$ is a basis for $T_p^*M$?

Published on 19 Mar 2026 - 16:57

156

Views

Tangent space definition in Algebraic Geometry

Published on 24 Mar 2026 - 21:53

91

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Clarification in definition tangent vector

Published on 08 Oct 2019 - 16:30

265

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(Algebraic) derivations $\frac{\partial}{\partial x_j}$ are linearly independent

Published on 03 Mar 2026 - 16:46

84

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Show that if image of a connected $2$ surface under Gauss map is a single point on unit sphere then $S$ is a part of a plane.

Published on 21 Oct 2019 - 17:32

266

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Proof of the tangent plane

Published on 23 Oct 2019 - 4:00

53

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analyze constrained extremum by projection to tangent space

Published on 24 Oct 2019 - 10:58

64

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Tangent space of lie subgroup

Published on 26 Oct 2019 - 23:30

89

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Differential forms vanishing at $T_p\mathbb S^2$

Published on 06 Mar 2026 - 7:48

112

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Orientation induced on tangent plane

Published on 02 Nov 2019 - 1:24

36

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Confusion regarding relation in differential geometry

Published on 02 Nov 2019 - 12:45

378

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Canonical/tautological 1-form

Published on 07 Nov 2019 - 17:10

736

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A general formula for the parametrisation of the tangent space (in $\Bbb{R}^n$)

Published on 08 Nov 2019 - 19:40

146

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Find equation of tangential plane at a given point of a surface

Published on 12 Nov 2019 - 16:33

74

Views

If $(f_)_p(v_p) = (f_)_p(w_p)$ for all $f\in C^\infty(M)$, then $v_p = w_p$.

Published on 12 Nov 2019 - 20:33

List Question

Is the matrix $dF_p$ invertible when $F=(y^1, \dots, y^n)$ and $(dy^1\big|_p,\dots, dy^n\big|_p)$ is a basis for $T_p^*M$?

Tangent space definition in Algebraic Geometry

Clarification in definition tangent vector

(Algebraic) derivations $\frac{\partial}{\partial x_j}$ are linearly independent

Show that if image of a connected $2$ surface under Gauss map is a single point on unit sphere then $S$ is a part of a plane.

Proof of the tangent plane

analyze constrained extremum by projection to tangent space

Tangent space of lie subgroup

Differential forms vanishing at $T_p\mathbb S^2$

Orientation induced on tangent plane

Confusion regarding relation in differential geometry

Canonical/tautological 1-form

A general formula for the parametrisation of the tangent space (in $\Bbb{R}^n$)

Find equation of tangential plane at a given point of a surface

If $(f_)_p(v_p) = (f_)_p(w_p)$ for all $f\in C^\infty(M)$, then $v_p = w_p$.

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