Existence and Nonexistence of Warped Product Submanifolds of Almost Contact Manifolds

Year 2023, , 367 - 378, 30.04.2023

Abdulqader Mustafa , Cenap Ozel , Alexander Pigazzini , Richard Pincak

https://doi.org/10.36890/iejg.1131334

Abstract

This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both known and new results. Moreover, a discrete example of contact $CR$-warped product submanifold in Kenmotsu manifold is constructed. For further research direction, we addressed a couple of open problems arose from the results of this paper.

Keywords

Contact $CR$-warped products, Sasakian manifolds, Kenmotsu manifolds, cosymplectic manifolds, nearly trans-Sasakian manifolds, general warped product, doubly warped product, second fundamental form, totally geodesic

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