We establish a general inequality for the squared norm of second fundamental form of these types of submanifolds.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data: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 $_fM^{\theta}\times_{b}M^{T}$.
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Conclusion & Impact:We establish a general inequality for the squared norm of second fundamental form of these types of submanifolds.
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.
Aydın, S. G., Taştan, H. M. (2022). Conformal-twisted product semi-slant submanifolds in globally conformal Kaehler manifolds. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1028–1046. https://ajindex.com/articles/529454
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