On the existence of a generalized class of recurrent manifolds

Absos Ali Shaikh; Indranil Roy; Haradhan Kundu

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arXiv · 1504.02534

On the existence of a generalized class of recurrent manifolds

Absos Ali Shaikh·Indranil Roy·Haradhan Kundu

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Abstract

The present paper deals with the proper existence of a generalized class of recurrent manifolds, namely, hyper-generalized recurrent manifolds. We have established the proper existence of various generalized notions of recurrent manifolds. For this purpose we have presented a metric and computed its curvature properties and finally we have obtained the existence of a new class of semi-Riemannian manifolds which are non-recurrent but hyper-generalized recurrent, Ricci recurrent, conharmonically recurrent, manifold of recurrent curvature 2-forms and semisymmetric; not weakly symmetric but weakly Ricci symmetric, conformally weakly symmetric and conharmonically weakly symmetric; non-Einstein but Ricci simple; do not satisfy $P\cdot P =0$ but fulfills the condition $P \cdot P = -\frac{1}{3}Q(S, P)$, $P$ being the projective curvature tensor.

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Absos Ali Shaikh, Indranil Roy, Haradhan Kundu. 2015-04-10. On the existence of a generalized class of recurrent manifolds. https://arxiv.org/abs/1504.02534

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