Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2015, Article ID 458178, 13 pages
http://dx.doi.org/10.1155/2015/458178
Research Article

Hypersurface Constrained Elasticae in Lorentzian Space Forms

1Department of Mathematics, Faculty of Science and Technology, Apartado 644, 48080 Bilbao, Spain
2Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-701, Republic of Korea

Received 30 August 2015; Accepted 13 October 2015

Academic Editor: Pavel Kurasov

Copyright © 2015 Óscar J. Garay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study geodesics in hypersurfaces of a Lorentzian space form , which are critical curves of the -bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesic and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3-space foliated by critical geodesics.