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New York Journal of Mathematics
Volume 26 (2020), 1338-1354

  

Garima Gupta, Rakesh Kumar, and Rakesh Kumar Nagaich

Geometry of semi-invariant lightlike product manifolds

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Published: November 15, 2020.
Keywords: Semi-invariant lightlike submanifolds, indefinite Kaehler manifolds, quarter-symmetric non-metric connections, totally umbilical lightlike submanifolds.
Subject: 53B30, 53B35, 53C05.

Abstract
We study the geometry of semi-invariant lightlike submanifolds of an indefinite Kaehler manifold M admitting a quarter-symmetric non-metric connection D. We establish conditions for a proper totally umbilical semi-invariant lightlike submanifold of M admitting D to be a totally geodesic semi-invariant lightlike submanifold. We further derive some characterization theorems for a semi-invariant lightlike submanifold of M admitting D to be a semi-invariant lightlike product manifold. Finally, we obtain some necessary and sufficient conditions for a semi-invariant lightlike submanifold of M admitting D to be a minimal lightlike submanifold.

Acknowledgements

The authors would like to express our sincere gratitude to the referees of our paper for their valuable suggestions.


Author information

Garima Gupta:
Department of Basic and Applied Sciences
Punjabi University
Patiala, Punjab, India

garima@pbi.ac.in

Rakesh Kumar:
Department of Basic and Applied Sciences
Punjabi University
Patiala, Punjab, India

dr_rk37c@yahoo.co.in

Rakesh Kumar Nagaich:
Department of Mathematics
Punjabi University
Patiala, Punjab, India

nagaich58rakesh@gmail.com