On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds


Deszcz R., Głogowska M., Hotlos M., Şentürk Z.

5th International Conference of Mathematical Sciences, ICMS 2021, İstanbul, Turkey, 23 - 27 June 2021, vol.2483 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 2483
  • Doi Number: 10.1063/5.0118057
  • City: İstanbul
  • Country: Turkey
  • Keywords: 2-quasi-Einstein manifold, Einstein manifold, generalized Einstein metric condition, pseudosymmetry type curvature condition, quasi-Einstein manifold, warped product manifold
  • Istanbul Technical University Affiliated: Yes

Abstract

© 2022 American Institute of Physics Inc.. All rights reserved.The tensor R · C − C · R and the tensors Q(g, R), Q(S, R), Q(g, C) and Q(S, C) of every Einstein manifold (M, g), n ≥ 4, satisfy R · C − C · R = (κ/((n − 1)n)) Q(g, R) = (κ/((n − 1)n)) Q(g, C) = (1/(n − 1)) Q(S, R) = (1/(n − 1)) Q(S, C). Motivated by this we study curvature properties of non-Einstein and non-conformally flat semi-Riemannian manifolds of dimension ≥ 4 satisfying the following family of generalized Einstein metric conditions: the tensor R· C − C · R is a linear combination of the tensors Q(g, R), Q(S, R), Q(g, C), Q(S, C), Q(g, g ∧ S ) and Q(S, g ∧ S ). We present results on quasi-Einstein and 2-quasi-Einstein warped product manifolds satisfying particular conditions of these family of conditions.