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Can $dF_p:T_pM\to T_{F(p)}N$ be surjective?

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#manifolds #smooth-manifolds #manifolds-with-boundary
115
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$C^{r-1}$ Diffeomorphisms on $C^r$ manifolds

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#manifolds #smooth-manifolds #diffeomorphism
111
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Question about connected manifold

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#differential-geometry #manifolds #connectedness #submanifold #transversality
1.8k
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De Rham cohomology of compact manifold minus one point

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#differential-geometry #manifolds #homology-cohomology #de-rham-cohomology
138
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Tensor Analysis On Manifolds: Question on an example manifold

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#differential-geometry #manifolds #tensors
200
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Understanding the Proof about the Uniqueness of $d$ operator

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#geometry #differential-geometry #manifolds #proof-explanation #tensors
575
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Compute the exterior product of $n$ copies of $\omega=dx_1 \wedge dx_2+\cdots+dx_{2n-1}\wedge dx_{2n}$

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#multivariable-calculus #manifolds #differential-forms
89
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What happens if I glue a Möbius strip to a sphere with a hole in it?

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#general-topology #manifolds
253
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Example of a symmetric manifold without rotation symmetry?

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#manifolds #symmetry
69
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Why $\dim(\ker T_z f)=\dim(T_z(f^{-1}(c)))$?

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#manifolds #smooth-manifolds #submanifold #tangent-spaces
290
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Intuitively what are submanifolds?

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#differential-geometry #manifolds #smooth-manifolds #submanifold
84
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Is my argument for $dy\wedge dz + dz\wedge dx + dx \wedge dy = \big(\sum_i(g_u\wedge g_v)_i\big)du\wedge dv$ correct?

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#multivariable-calculus #differential-geometry #manifolds #vector-analysis #differential-forms
403
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Smooth map between smooth manifold and boundary of manifold

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#manifolds #smooth-manifolds #manifolds-with-boundary
501
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A characterization of tangent space to level set of a smooth submersion

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#manifolds #smooth-manifolds
84
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A PL version of Urysohn’s Lemma

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#manifolds #smooth-manifolds

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