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GP $1.2.9(d)$: $d(f\times g)_{(x,y)}=df_x\times dg_y$

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#derivatives #manifolds #differential-topology #smooth-manifolds
255
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Integral foliation identity

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#real-analysis #integration #differential-geometry #manifolds #lebesgue-integral
704
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Characterization of the tangent space in terms of velocity vectors

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#real-analysis #manifolds #differential-topology #smooth-manifolds
711
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GP $1.2.11(b)$: Tangent space to the graph of a smooth function

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#real-analysis #manifolds #differential-topology #smooth-manifolds
2k
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Calculating the tangent space to a hyperboloid

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#real-analysis #manifolds #differential-topology #smooth-manifolds
213
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Let $M$ be a compact manifold of pos. dimension and let $p \in M$. Show that $M$ is homeomorphic to the one-pt compactification of $M \setminus \{p\}$

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#general-topology #manifolds
138
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Differential of a smooth extension of a map

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#real-analysis #manifolds #differential-topology #smooth-manifolds
20
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Statement of GP $1.2.12$: velocity vectors

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#real-analysis #manifolds #differential-topology #smooth-manifolds
336
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space of d variate polynomial of degree at most n restricted to a manifold in R^d

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#polynomials #manifolds
228
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When we construct a regular sub manifold, can we set any coordinate of the coordinate system equal to 0?

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#differential-geometry #manifolds #differential-topology
138
Views

Complex projective line 1

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#manifolds #inverse #smooth-manifolds #complex-geometry #projective-space
110
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Degree of a map $f: S^3 \times S^1 \to S^4$ which is odd with respect to $S^3$

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#algebraic-topology #manifolds #differential-topology
135
Views

How can I understand the regular point or the regular level set from a geometry view?

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#differential-geometry #manifolds #differential-topology #smooth-manifolds
759
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Differential $1$ forms as linear maps

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#differential-geometry #manifolds #smooth-manifolds #differential-forms #vector-fields
1.1k
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Compact support of a p-form?

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#real-analysis #analysis #differential-geometry #manifolds

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