Contact Lorentzian Manifolds of Constant Curvature and CR-Manifolds

  • Mohamed H. A. Hamed
  • Islam F. M. Osman
  • Mohammed B.A. Mohammad
  • Arafat Abdelhameed Abdelrahmann
  • Asmaa Eltayeb Ali Elhassan
Keywords: Contact Lorentzian structures, Lorentzian metrics, Constant sectional curvature, Non-degenerate CR structures

Abstract

In this work, we show that a contact Lorentzian manifolds of dimension(2n + 1),n ≥ 2,has constant sectional curvaturek, then the structure(M ̅(2n+1),ϕ ̅,ξ,η,g ̅)is Sasakian and k=-1=g ̅( ξ ,ξ),where ξ is characteristic vector field. We present some notions of contact Lorentzian structure with a non-degenerate almost CR manifolds. Moreover, we given some an examples of contact Lorentzian manifolds with condition trace h2 = 0.

References

Blair D.E., Calvaruso G, Perrone D. (2010). Riemannian Geometry of Contact and Symplectic Manifolds, Progr. Math. Birkh¨auser, Boston.

Calvaruso G, and D. Perrone (2010). Contact Pseudo-metric manifolds, ifferential Geom. Appl. 28, 615-634.

Calvaruso G. , and D. Perrone. (2013). Erratum to: Contact Pseudo-metric anifolds, [Differential Geom. Appl. 28 (2010), 615-634], Differential Geom. Appl. 31 (2013), 836-837.

Calvaruso,G. (2011). Contact Lorentzian manifolds, Differential Geom. Appl. 29: 641-551 .

Dragomir S., M. Hasan and F. Al-Solamy (2016). Geometry of Cauch-Riemann Submanifolds, Springer.

Hamed M.. A. Hamed, F. Massamba and S. Ssekajja, On null submanifolds of generalized Robertson-Walker space forms, Turk. J. Math. 43 (2019), 1650-1667.
Olszak Z., On contact metric manifolds, Tˆohoku Math. J. 31 (1979) 247-353.

Perrone D. (2014), Curvature of K-contact semi-Riemannian manifolds, Can. Math. Bull.

Perrone D. (2014)., Contact Pseudo-metric manifolds of constant curvature and CR geometry, Results. Math. 66 : 213-225.

Takahashi T. (1969). , Sasakian manifold with Pseudo-Riemannain metrics, Tˆohoku Math. J. 21 :271-290.
Published
2022-02-08