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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\looseness -1
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\looseness -1
Summary:
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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