On Z-Symmetric Manifold Admitting Projective Curvature Tensor


Yavuz Tasci A., Zengin F.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, vol.15, no.1, pp.39-46, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.36890/iejg.986956
  • Journal Name: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.39-46
  • Keywords: Projective curvature tensor, Z-symmetric tensor, Codazzi tensor, recurrent tensor
  • Istanbul Technical University Affiliated: Yes

Abstract

The object of the present paper is to study the Z-symmetric manifold with the projective curvature tensor. At first, we study the case of Z-tensor and projective Ricci tensor being of Codazzi type. Next, we consider recurrent Z-tensor and recurrent projective Ricci tensor. We also study the Z-symmetric manifold with projective curvature tensor with divergence-free Z-tensor. Finally, we construct an example of the Z-symmetric manifold with projective curvature tensor.