• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.979-994
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• 2014

We study half lightlike submanifold M of an indefinite trans-Sasakian manifold such that its structure vector field is tangent to M. First we study the general theory for such half lightlike submanifolds. Next we prove some characterization theorems for half lightlike submanifolds of an indefinite generalized Sasakian space form.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.615-632
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• 2019

We study generic lightlike submanifolds M of an indefinite trans-Sasakian manifold ${\bar{M}}$ or an indefinite generalized Sasakian space form ${\bar{M}}(f_1,f_2,f_3)$ endowed with an $({\ell},m)$-type metric connection subject such that the structure vector field ${\zeta}$ of ${\bar{M}}$ is tangent to M.

• East Asian mathematical journal
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• v.30 no.1
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• pp.1-14
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• 2014

The first purpose of this paper is to study contact CR submanifolds of Sasakian manifolds and investigate some properties concernig with ${\phi}$-holomorphic bisectional curvature. The second purpose is to show an existence theorem of mixed foliate proper contact CR submanifolds in the standard Sasakian space form $E^{2m+1}$(-3) with constant ${\phi}$-sectional curvature -3.

• East Asian mathematical journal
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• v.9 no.2
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• pp.283-294
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• 1993

• Kyungpook Mathematical Journal
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• v.26 no.2
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• pp.119-128
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• 1986

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1315-1328
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• 2019

The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.

• Communications of the Korean Mathematical Society
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• v.6 no.1
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• pp.119-133
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• 1991

• Journal of the Korean Mathematical Society
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• v.30 no.2
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• pp.299-313
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• 1993

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.395-406
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• 2007

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for an integral submanifold of an S-space form. By polarization, we get a basic inequality for Ricci tensor also. Equality cases are also discussed. By giving a very simple proof we show that if an integral submanifold of maximum dimension of an S-space form satisfies the equality case, then it must be minimal. These results are applied to get corresponding results for C-totally real submanifolds of a Sasakian space form and for totally real submanifolds of a complex space form.