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3
votes
2answers
173 views

Converse to Chow's theorem in sub-riemannian geometry

Chow's theorem is the statement that if $M$ is a connected smooth manifold endowed with a distribution $\mathcal{D}$ which is completely non integrable (i.e. iterated commutators of smooth sections of ...
8
votes
3answers
356 views

twisted Poisson structures, degenerate metrics and integrability properties of (2,0)-tensors

Given a regular (constant rank) bi-vector $\Pi \in \Gamma(\bigwedge^2TM)$ on a smooth manifold $M$ the necessary and sufficient condition for the image of $\Pi^\sharp:T^*M\to TM$ to be an integrable ...
2
votes
1answer
184 views

Local (quasi-)normal form for 3-plane fields on 6-manifolds

A 3-plane field $D$ on a 6-manifold $M$ is generic if $[D, D] = TM$. I'd like to do some explicit computations with a general local plane field of this type, and so I want to find a local ...
2
votes
1answer
361 views

Osculating spaces and distributions on (real) Grassmannian manifold

Hello! Recenlty, doing my research, I came across a quite natural construction, and I would like to know more about it. Unfortunately, being not expert neither in Grassmannians nor in Contact ...
4
votes
1answer
616 views

Studying non-linear PDEs with manifolds

I'm sorry if this is an inappropriate forum to ask this question on, for I fear it is pretty undergraduate-level one :) I was contemplating on the study of non-linear PDEs. Is it possible to reduce a ...
7
votes
2answers
316 views

Hypersurfaces orthogonal to a cone

This question is somewhat related to Differential inclusions for distributions. but I am asking for something rather more specific, so I hope it is alright to leave this as a separate, new question. ...
1
vote
0answers
118 views

Differential inclusions for distributions.

Given a set valued function $F$ such that for every $x\in M$ (a manifold) we have that $F(x)\subset T_xM$, a differential inclusion is the "equation", $\dot{x} \in F(x)$. I was wondering if someone ...
2
votes
1answer
307 views

Integrability of distributions close to a given one.

In this and this papers Thurston proves that every distribution is homotopic to an integrable one (in the first one for codimension greater than one and in the other for codimension one). Recently, ...
0
votes
1answer
238 views

Does a smooth, constant-rank, integrable distribution have a basis in which the traces of the structure constants are the divergences of the corresponding basis elements?

In a previous question, I asked an utterly trivial question, which Deane Yang correctly pointed out was utterly trivial. I will now ask a similar question, which is the one I meant to ask last time; ...
0
votes
1answer
177 views

Does every smooth integrable constant-rank distribution have a basis in which the structure constants are traceless?

My question is local and coordinate-full: I have an open neighborhood $0 \in U \subseteq \mathbb R^n$, and I'm allowed to make it smaller around $0$. On this neighborhood, I have a constant-rank-$k$ ...