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arXiv · 1204.6125

Warped product contact CR-submanifolds of globally framed f-manifolds with Lorentz metric

Khushwant Singh·S. S. Bhatia
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Abstract

In the present paper, we study globally framed f-manifolds in the particular setting of indefinite S-manifolds for both spacelike and timelike cases. We prove that if $M = N^{\perp} \times_f N^T$ is a warped CR-submanifold such that $N^{\perp}$ is $ϕ$?-anti-invariant and NT is $ϕ$?-invariant, then M is a CR-product. We show that the second fundamental form of a contact CR warped product of a indefinite S space form satisfies a geometric inequality, $\|h\|^2 \geq p{3\|\nabla lnf\|^2 - \triangle lnf + (c + 2)k + 1}$.

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Khushwant Singh, S. S. Bhatia. 2012-04-27. Warped product contact CR-submanifolds of globally framed f-manifolds with Lorentz metric. https://arxiv.org/abs/1204.6125

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