The curvature tensor of -contact metric manifolds

ARSLAN K. , Carriazo A., Martin-Molina V., MURATHAN C.

MONATSHEFTE FUR MATHEMATIK, vol.177, no.3, pp.331-344, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 177 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.1007/s00605-015-0762-3
  • Title of Journal : MONATSHEFTE FUR MATHEMATIK
  • Page Numbers: pp.331-344
  • Keywords: (kappa, mu, nu)-contact metric manifold, Generalized (kappa, mu, nu)-space form, Contact metric manifold, D-a-homothetic deformation, Conformal flatness, (KAPPA, FORMS

Abstract

We study the Riemann curvature tensor of -contact metric manifolds, which we prove to be completely determined in dimension 3. We also observe how this curvature tensor is affected by -homothetic deformations, which will prompt the definition and study of generalized -space forms and of the necessary and sufficient conditions for them to be conformally flat.