Dirac Operators on Time Flat Submanifolds with Applications

Oussama Hijazi (1) , Sebastián Montiel , Simon Raulot (2)

1 IECL - Institut Élie Cartan de Lorraine
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this paper, we study Dirac-type operators on time flat submanifolds in spacetimes satisfying the Einstein equations with non positive cosmological constant. We apply our results to obtain global rigidity results for n-dimensional time flat submanifolds in the Minkowski spacetime as well as in the anti-de Sitter spacetime.

Domaines: Physique mathématique [math-ph]

Oussama Hijazi, Sebastián Montiel, Simon Raulot. Dirac Operators on Time Flat Submanifolds with Applications. Commun.Math.Phys., 2017, 351 (3), pp.1177-1194. ⟨10.1007/s00220-017-2837-6⟩. ⟨hal-01554635⟩