Mathematics Subject Classification (2000): 53C25, 53C40, 53C42.

In this paper, warped product CRCR-submanifolds in Kahler manifolds and contact Sasakian, Kenmotsu cosymplectic manifolds, are shown to possess a geometric property; namely DTDT-minimal. Taking benefit from property, an optimal general inequality is established by means of the Gauss equation, we leave cosyplectic because it easy structure. Moreover, rich geometry appears when necessity sufficie...

* Correspondence: meraj79@gmail. com Department of Mathematics, University of Tabuk, Tabuk, Kingdom of Saudi Arabia Full list of author information is available at the end of the article Abstract In this article, we have obtained necessary and sufficient conditions in terms of canonical structure F on a semi-invariant submanifold of an almost contact manifold under which the submanifold reduced...