315 reputation
18
bio website
location Silesia, Czech Republic
age 35
visits member for 2 years, 4 months
seen yesterday

Reasonably expert in Differential Geometry, I work mostly with jet bundles and their natural structures trying to exploit them in the areas of nonlinear PDEs and Calculus of Variations.


Jul
16
comment Symmetry analysis of differential equations
The standard reference on this concern is Michor's book mat.univie.ac.at/~michor/… Anyway, I would guess that there are only two homotopy types: the orientation-preserving and the orientation-reversing. The identical transformation is the diagonal of $\mathbb{R}^2$, and I don't see any reason why it shouldn't be possible to deform the graph of any other orientation-preserving transformation to the diagonal.
Jul
11
comment Euler Class of a vector field
@HenryT.Horton: why do you need to pass to a 2-plane field? Besides, in the question there are no metrics mentioned, so you cannot take "orthogonal"... What about the line bundle spanned by $X$? I think in this case, the Euler class just tells whether $X$ is nowhere vanishing or not (e.g., if I'm not mistaken, on the 2-sphere all fields should have nonzero Euler class).
Jul
9
answered Generalized Leibniz rule
Jul
7
awarded  Nice Question
Jul
4
comment Is there a “unique” homogeneous contact structure on odd-dimensional spheres?
@RobertBryant : following your comment, I added a long edit to the original question.
Jul
4
revised Is there a “unique” homogeneous contact structure on odd-dimensional spheres?
Added a long edit following R. Bryant's last remark.
Jul
2
awarded  Curious
Jun
26
comment Is there a “unique” homogeneous contact structure on odd-dimensional spheres?
@OldřichSpáčil : I did not know this overtwisted/tight dichotomy - thank you for pointing it out. I'm going to give a look at the references you've suggested!
Jun
25
comment Is there a “unique” homogeneous contact structure on odd-dimensional spheres?
Before posting on MO I asked my questions to Dmitri Alekseevsky, who also claimed that "your problems can be easily solved just by looking at Berger classification". Still, I don't understand how (spheres are symmetric spaces and not covered by Berger). Anyway, if it is so easy, why nobody can tell me, e.g., if there are other ways to write down $S^5=G/H$, with $G$ different than $SO(6)$ and $SU(3)$? (Of course, I'll skip here the above remarks on compactness of $G$).
Jun
25
comment Is there a “unique” homogeneous contact structure on odd-dimensional spheres?
@FabriceBaudoin I wasn't aware of Bland and Duchamp's works: thank you for pointing them out. They'll certainly help in facing my first side question.
Jun
24
asked Is there a “unique” homogeneous contact structure on odd-dimensional spheres?
Jun
10
accepted What is the total polarization of the determinant?
Jun
10
revised What is the total polarization of the determinant?
added 717 characters in body
Jun
4
revised What is the total polarization of the determinant?
Removed exponent "$n$" from "$\mathbb{R}$" in the last displayed formula
May
29
revised What is the total polarization of the determinant?
Added 2 tags
May
28
answered Discovering and selecting conferences
May
27
awarded  Yearling
May
27
asked What is the total polarization of the determinant?
May
17
accepted Is the Lie quadric $Q^3$ isomorphic to the Lagrangian Grassmannian $LG(2,4)$?
May
12
revised Is the Lie quadric $Q^3$ isomorphic to the Lagrangian Grassmannian $LG(2,4)$?
I just set $n=3$ in the notation $Q^n$ (before it was 2), since it should match the dimension of the quadric rather than the dimension of the space the spheres live in.