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Journal of Geometry

, 110:56 | Cite as

Second order parallel tensors on singular quasi-constant curvature manifolds

  • Ramesh SharmaEmail author
Article
  • 46 Downloads

Abstract

Extending the result for the regular case (i.e. Ricci curvature along the generating vector field does not vanish) to the singular case, we have presented a classification of second order parallel tensors on a non-flat manifold of quasi-constant curvature manifolds and applied it to classify parallel and affine Killing vector fields on those manifolds.

Keywords

Second order parallel tensor Quasi-constant curvature Parallel vector field Affine Killing vector field 

Mathematics Subject Classification

53 C20 53C 21 53 C25 

Notes

Acknowledgements

The author is grateful to the reviewer for valuable suggestions toward the improvement of this work.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of New HavenWest HavenUSA

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