Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds

Abstract

We introduce the notion of conformal-twisted product submanifolds of the form $_fM^{T} times_{b}M^{ theta}$ and $_fM^{ theta} times_{b}M^{T}$, where $M^T$ is a holomorphic submanifold and $M^ theta$ is a proper slant submanifold of $M$ in a globally conformal Kaehler manifold and $f$ and $b$ are conformal factor and twisting function, respectively. We give necessary and sufficient conditions for proper semi-slant submanifold to be a locally conformal-twisted product for such submanifolds of the form $_fM^{T} times_{b}M^{ theta}$ and $_fM^{ theta} times_{b}M^{T}$. We establish a general inequality for the squared norm of second fundamental form of these types of submanifolds.