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...

This paper consists of two main sections. In the first part, we give some general information about almost contact manifold, α−Sasakian, β−Kenmotsu and trans-Sasakian Structures on manifolds. second these structures were expressed tangent bundle with help lifts most forms tried to be obtained.

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.