8
votes
3answers
325 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 $\Pi^\sharp:T^*M\to TM$ t …
2
votes
1answer
168 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 …
2
votes
1answer
276 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 …
4
votes
1answer
574 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 p …
7
votes
2answers
295 views
Hypersurfaces orthogonal to a cone
This question is somewhat related to http://mathoverflow.net/questions/37524/differential-inclusions-for-distributions but I am asking for something rather more specific, so I hope …
2
votes
1answer
256 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 codimensio …
0
votes
1answer
220 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 mean …
0
votes
1answer
161 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 …
0
votes
0answers
111 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 w …
