• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.965-977
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• 2016

The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give necessary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product submanifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are obtained.

• 대한수학회보
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• 제52권1호
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• pp.215-222
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• 2015

We show that homology group on a contact CR-warped product submanifold in odd dimensional sphere is zero under certain conditions in terms of warping function and the dimension of the submanifold.

• 대한수학회보
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• 제51권3호
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• pp.863-881
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• 2014

Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

• 대한수학회논문집
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• 제34권4호
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• pp.1303-1313
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• 2019

Recently Hui et al. ([8,9]) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. The characterization for both these classes of warped product submanifolds have been studied here. It is also shown that there do not exists any proper warped product bi-slant submanifold of a $(LCS)_n$-manifold. Although the existence of a bi-slant submanifold of $(LCS)_n$-manifold is ensured by an example.

• 대한수학회지
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• 제42권5호
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• pp.1101-1110
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• 2005

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.