Mathematica Bohemica, Vol. 147, No. 3, pp. 419-434, 2022
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.
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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
