INVARIANT VARIATIONAL PROBLEMS ON CONFORMAL WORLDLINES IN EINSTEIN UNIVERSE
Keywords:
Lorentz geometry, Einstein universe, timelike curves, conformal strain functional, conformal worldlinesAbstract
The purpose of this paper is to investigate conformally invariant variational problem for timelike curves in the higher dimensional Einstein universe. Lorentz analogue of the conformally invariant functional in Riemannian case provides computation of the Euler-Lagrange equations for critical curves which are called as worldlines.
References
E. Musso and L. Nicolodi. Conformal deformation of spacelike surfaces in minkowski space. Houston J. Math. 35, no. 4, pages 68–85, 2009..
E. Musso. Closed trajectories of the conformal arclength functional. Journal of Physics: Conference Series 410, page 012031, 2013.
E. Musso and L. Nicolodi. Quantization of the conformal arclength functional on space curves. Comm. Anal. Geom. 25, pages 209–242, 2017.
U. Hertrich-Jeromin. Introduction to Möbius differential geometry. 2003.
L. Mari M. Magliaro and M. Rigoli. On the geometry of curves and conformal geodesics in the möbius space. Ann. Global Anal. Geom. 40, pages 133–165, 2011.
E. Musso O. Eshkobilov and L. Nicolodi. Critical Robertson-walker universes. Differential Geom. Appl. 66, pages 23–41, 2019.
T. Drumm W. M. Goldman T. Barbot, V. Charette and K. Melnick. A premier on the (2+1)-einstein universe. Recent developments in pseudo-Riemannian geometry, pages 179–229, 2008.
E. Musso A. Dzhalilov and L. Nicolodi. Conformal geometry of timelike curves in the (1+2)-einstein uni-verse. Nonlinear Anal. 143, pages 224–255, 2016.
E. Musso O. Eshkobilov and L. Nicolodi. On the restricted conformal group of the (1+n)-einstein static universe. J. Geom. Phys. 146, pages 1–25, 103517, 2019.
E. Musso O. Eshkobilov and L. Nicolodi. The geometry of conformal timelike geodesics in the einstein universe. Journal of Mathematical Analysis and Applica-tions, page 124730, 2021.
