On the 17th of May 2018, at 10:15 a.m.
Giovanni Moreno (KMMF WFUW)
will give a talk on
"The equations of generalised Weingarten hypersurfaces are the invariant k-th order PDEs over homogeneous (k-1)-jet spaces"
Abstract
Let M be an (n+1)-dimensional manifold and let a group G act transitively on M. I am going to make two assumptions about this action. First, I assume that there exists a hypersurface S0 of M, such that the G-orbit of the (k-1)-st jet of S0 in a point o of M is open in Jk-1(n,M) and, second, I assume that there are no open G-orbits in Jk(n,M). Then, starting from such an S0, I will construct a family of (scalar) G-invariant k-th order PDEs in n independent variables and 1 dependent variable. I will show that the solutions to these equations are a natural analogue of the Weingarten surfaces in the three-dimensional Euclideam space. I will discuss in detail the cases when k=2 or k=3. I will also find convenient coordinates to locally describe the so-obtained equations.
The seminar takes place on Thursdays from 10:15 a.m. to 12:00
in the room 2.23 of the main building of the Faculty of Physics (the 2nd floor), Pasteur Str. 5,
Warszawa.
Additional information can be found on the webpage
http://oldwww.fuw.edu.pl/KMMF/sem.czw.przedp.html.
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