Rank k vector distribution D on the manifold M is by definition a k-dimensional subbundle of the tangent bundle TM. In other words, for each point q in M a k-dimensional subspace D(q) of the tangent space T_qM is chosen and D(q) depends smoothly on q. Two vector distributions D_1 and D_2 are called locally equivalent at some point q_0 in M , if there exists a diffeomorphism F of some neighbourhood U of q_0, which transforms distribution D_1 to D_2, i.e., F_*D_1(q)=D_2 (F(q)) for all q in U. The question is when two distributions are locally equivalent? In the present talk we will restrict ourselves to the case k=2. If dim M=3 or 4, all generic germs of rank 2 distributions are equivalent (Darboux's and Engel's theorems). If dim M >= 5, the normal forms of these germs contain (dim M-4) functional parameters. Using the general theory of curves in the Lagrange Grassmannian developed in [1], we will describe the construction of basic invariant of the distribution, fundamental form, which is the obstacle to local equivalence. The case dim M=5 will be discussed in greater details. References [1] A. Agrachev, I. Zelenko, Geometry of Jacobi curves.I, J. Dynamical and Control Systems, 8(1):93-140,
You are here
Nearly critical semilinear elliptic problems.
Research Group:
Speaker:
Manuel Del Pino M.
Institution:
Universidad de Chile
Schedule:
Thursday, February 15, 2001 - 10:00 to 11:00
Location:
Room L
Abstract:
Links
- Call of interest for positions in mathematics at SISSA
- Public Calls for Professors
- Temporary Researchers
- Temporary Technologists
- Research Fellowships
- Open positions in MathLab
- SISSA Mathematical Fellowships
- PhD Scolarships
- SIS Fellowships
- Pre-PhD Fellowships
- MSc in Mathematics
- Master Degree in Data Science and Scientific Computing
- Professional Master Courses
- SISSA Mathematics Medals
- SISSA Springer Series
Upcoming events
-
Daniel Hernández Ruipérez
Algebraic supergeometry and moduli of stable supermaps
Tuesday, February 18, 2025 - 16:00
-
Jinpeng Lu
On the stability of Gel'fand's inverse problem
Wednesday, February 19, 2025 - 14:00
-
Wei Cheng
Singularity Propagation: Dynamic and Transport Perspectives
Wednesday, February 26, 2025 - 14:00 to 15:00
-
Daniel Hernández Ruipérez
Algebraic supergeometry and moduli of stable supermaps
Tuesday, February 18, 2025 - 16:00
Today's Lectures
-
09:00 to 11:00
-
09:00 to 11:00
Recent publications
-
G.P. Leonardi; G. Saracco,Rigidity and trace properties...
-
S. Bianchini; G.Maria Leccese,Existence and blow-up for non-...
-
M. Berti; S. Cuccagna; F. Gancedo; S. Scrobogna,Paralinearization and extended...
-
G. Ortali; F. Toschi; J.W. van de Meent,Modeling Droplets Dynamics in...