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

Year 2021, Volume: 50 Issue: 4, 1028 - 1046, 06.08.2021

Sibel Gerdan Aydın Hakan Mete Taştan

https://doi.org/10.15672/hujms.801651

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.

Keywords

twisted product manifold, holomorphic ditribution, locally and globally conformal Kaehler manifold, semi-slant submanifold, slant distribution

Supporting Institution

TUBITAK

Project Number

119F179

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