Second order parallel tensors on singular quasi-constant curvature manifolds
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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.
KeywordsSecond order parallel tensor Quasi-constant curvature Parallel vector field Affine Killing vector field
Mathematics Subject Classification53 C20 53C 21 53 C25
The author is grateful to the reviewer for valuable suggestions toward the improvement of this work.
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On behalf of all authors, the corresponding author states that there is no conflict of interest.
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