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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 $T_p^*M$?

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#differential-geometry #jacobian #tangent-spaces #co-tangent-space
159
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Tangent space definition in Algebraic Geometry

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#algebraic-geometry #definition #tangent-line #tangent-spaces
94
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Clarification in definition tangent vector

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#differential-geometry #definition #smooth-manifolds #tangent-spaces
267
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(Algebraic) derivations $\frac{\partial}{\partial x_j}$ are linearly independent

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#linear-algebra #abstract-algebra #partial-derivative #tangent-line #tangent-spaces
85
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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.

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#differential-geometry #surfaces #tangent-spaces
266
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Proof of the tangent plane

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#proof-writing #plane-curves #smooth-functions #tangent-spaces
55
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analyze constrained extremum by projection to tangent space

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#multivariable-calculus #manifolds #constraints #tangent-spaces
65
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Tangent space of lie subgroup

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#lie-groups #tangent-spaces
91
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Differential forms vanishing at $T_p\mathbb S^2$

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#differential-geometry #smooth-manifolds #tangent-spaces
113
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Orientation induced on tangent plane

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#differential-geometry #surfaces #tangent-spaces
37
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Confusion regarding relation in differential geometry

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#differential-geometry #manifolds #tangent-spaces
379
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Canonical/tautological 1-form

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#differential-geometry #symplectic-geometry #tangent-spaces
737
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A general formula for the parametrisation of the tangent space (in $\Bbb{R}^n$)

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#geometry #multivariable-calculus #differential-geometry #parametrization #tangent-spaces
147
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Find equation of tangential plane at a given point of a surface

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#real-analysis #differential-geometry #conic-sections #parametric #tangent-spaces
75
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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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#differential-geometry #smooth-manifolds #smooth-functions #tangent-spaces

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