bio | website | |
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location | Silesia, Czech Republic | |
age | 35 | |
visits | member for | 2 years, 3 months |
seen | 10 hours ago | |
stats | profile views | 502 |
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. |