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


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Gerdan Aydın S., Taştan H. M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.50, no.4, pp.1028-1046, 2021 (SCI-Expanded)

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.