#### Conference abstracts

Session B3 - Symbolic Analysis

July 15, 15:30 ~ 15:55 - Room B2

## Differential invariants for time-like curves and their applications to a conformally invariant variational problem.

### Emilio Musso

### Politecnico di Torino, Italy - emilio.musso@polito.it

In this talk I will focus on local differential invariants of a time-like curve with respect to the group of the Lorentz conformal transformations. The invariant of lower-order is a differential form of degree four (the "conformal strain") which, in turns, can be used to define natural parameterizations. When the conformal strain doesn't possesses zeroes, one can integrate its fourth root along the curve. This provides the simplest conformally invariant variational problem for time-like curves. I will give some hint on how to find the critical curves and I will discuss the existence of closed critical curves.

References

- E. Musso, L. Nicolodi, “Quantization of the conformal arclength functional on space curves”, Communications in Analysis and Geometry, to appear ; arXiv:1501.04101 [math.DG].

- A. Dzhalilov, E. Musso, L. Nicolodi, “Conformal geometry of time-like curves in the (1+2)-dimensional Einstein universe”, Nonlinear Analyisis Sereies A : Theory, Methods and Applications, 2016, Vol 143 p.224-255; arXiv:1603.01035 [math.DG].

- O. Eshkobilov, E.Musso, A conformally invariant variational problem for time-like curves, ArXiv 1566997 [mathDG 22 may 2016].

Joint work with L. Nicolodi (University of Parma, Italy), A. Dzhalilov (TTPU, Taschkent, Uzbekistan) and O. Eshkobilov (University of Torino, Italy).