• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1173-1192
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• 2013

We introduce CR, SCR and GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds and obtain their existence in indefinite nearly Kaehler manifolds of constant holomorphic sectional curvature $c$ and of constant type ${\alpha}$. We also prove characterization theorems on the existence of totally umbilical and minimal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1003-1016
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• 2023

In this paper, we introduce the idea of twisted product lightlike submanifolds of semi-Riemannian manifolds and provide non-trivial examples of such lightlike submanifolds. Then, we prove the non-existence of proper isotropic or totally lightlike twisted product submanifolds of a semi-Riemannian manifold. We also show that for a twisted product lightlike submanifold of a semi-Riemannian manifold, the induced connection ∇ is not a metric connection. Further, we prove that a totally umbilical SCR-lightlike submanifold of an indefinite Kaehler manifold ${\tilde{M}}$ does not admit any twisted product SCR-lightlike submanifold of the type M_⊥×_ϕM_T, where M_⊥ is a totally real submanifold and MT is a holomorphic submanifold of ${\tilde{M}}$. Consequently, we obtain a geometric inequality for the second fundamental form of twisted product SCR-lightlike submanifolds of the type M_T×_ϕM_⊥ of an indefinite Kaehler manifold ${\tilde{M}}$, in terms of the gradient of ln ϕ, where ϕ stands for the twisting function. Subsequently, the equality case of this inequality is discussed. Finally, we construct a non-trivial example of a twisted product SCR-lightlike submanifold in an indefinite Kaehler manifold.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.883-899
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• 2014

We introduce GCR-lightlike submanifold of a semi-Riemannian product manifold and give an example. We study geodesic GCR-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product. Finally, we discuss minimal GCR-lightlike submanifolds of a semi-Riemannian product manifold.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.289-304
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• 2021

In this paper, we establish several geometric characterizations focusing on the relationship between the squared norm of the second fundamental form and the warping function of SCR-lightlike warped product submanifolds in an indefinite Kaehler manifold. In particular, we find an estimate for the squared norm of the second fundamental form h in terms of the Hessian of the warping function λ for SCR-lightlike warped product submanifolds of an indefinite complex space form. Consequently, we derive an optimal inequality, namely $${\parallel}h{\parallel}^2{\geq}2q\{{\Delta}(ln{\lambda})+{\parallel}{\nabla}(ln{\lambda}){\parallel}^2+\frac{c}{2}p\}$$, for SCR-lightlike warped product submanifolds in an indefinite complex space form. We also provide one non-trivial example for this class of warped products in an indefinite Kaehler manifold.