Mathematica Bohemica, first online, pp. 1-16


Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold

Payel Karmakar

Received April 30, 2021.   Published online October 18, 2021.

Abstract:  The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, $\xi$-projectively flat, $M$-projectively flat, $\xi$-$M$-projectively flat, pseudo projectively flat and $\xi$-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, $M$-projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.
Keywords:  anti-invariant submanifold; trans-Sasakian manifold; Zamkovoy connection; $\eta$-Einstein manifold; Ricci curvature tensor; concircular curvature tensor; projective curvature tensor; $M$-projective curvature tensor; pseudo projective curvature tensor; Ricci soliton
Classification MSC:  53C05, 53C15, 53C20, 53C25, 53C40
DOI:  10.21136/MB.2021.0058-21

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Affiliations:   Payel Karmakar, Department of Mathematics, Jadavpur University, 188 Raja S. C. Mallick Road, Kolkata-700032, West Bengal, India, e-mail: payelkarmakar632@gmail.com


 
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