• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.149-165
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• 2018

A. Bejancu [2] was the first who instigated the new concept in differential geometry, i.e., CR-submanifolds. On the other hand, CR-submanifolds were generalized by B. Y. Chen [7] as slant submanifolds. Further, he gave the notion of a Kaehlerian slant submanifold as a proper slant submanifold. This article has two objectives. For the first objective, we derive Simons' type formula for a minimal Kaehlerian slant submanifold in a complex space form. Then, by applying this formula, we give a complete classification of a minimal Kaehlerian slant submanifold in a complex space form and also obtain its some immediate consequences. The second objective is to prove some results about semi-parallel submanifolds.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.829-841
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• 2020

The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study generalized quasi-conformally semi-parallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds and showed their existence by a non-trivial example. Among other it is shown that an invariant submanifold of a (LCS)n-manifold is totally geodesic if the second fundamental form is any one of (i) symmetric, (ii) recurrent, (iii) pseudo symmetric, (iv) almost pseudo symmetric and (v) weakly pseudo symmetric.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.1-10
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• 2014

In this paper, we study the curvature of locally symmetric or semi-symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$, whose structure vector field is tangent to M. After that, we study the existence of the totally geodesic screen distribution of half lightlike submanifolds of indefinite Kenmotsu manifolds with parallel co-screen distribution subject to the conditions: (1) M is locally symmetric, or (2) the lightlike transversal connection is flat.

• East Asian mathematical journal
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• v.31 no.1
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• pp.33-40
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• 2015

We study the geometry of r-lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the screen distribution of M is totally geodesic in M, and (b) at least one among the r-th lightlike second fundamental forms is parallel with respect to the induced connection of M. The main result is a classification theorem for irrotational r-lightlike submanifold of a semi-Riemannian manifold of index r admitting a semi-symmetric non-metric connection.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1089-1103
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• 2010

In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.

• Journal of the Korean Mathematical Society
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• v.24 no.2
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• pp.187-198
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• 1987

• Journal of the Korean Mathematical Society
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• v.25 no.2
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• pp.227-243
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• 1988

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.781-793
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• 2012

We study some properties of a semi-Riemannian submanifold of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Then, we prove that the Ricci tensor of a semi-Riemannian submanifold of a semi-Riemannian space form admitting a semi-symmetric non-metric connection is symmetric but is not parallel. Last, we give the conditions under which a totally umbilical semi-Riemannian submanifold with a semi-symmetric non-metric connection is projectively flat.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.705-717
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• 2013

In this paper, we study the geometry of half lightlike submanifolds M of a semi-Riemannian manifold $\tilde{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of $\tilde{M}$ is tangent to M, the screen distribution on M is totally umbilical in M and the co-screen distribution on M is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of M is parallel.

• East Asian mathematical journal
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• v.37 no.1
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• pp.41-77
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• 2021

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (��, ξ, η, g) in a complex space form Mn+1(c), c ≠ 0. We denote by Rξ = R(·, ξ)ξ and A(i) be Jacobi operator with respect to the structure vector field ξ and be the second fundamental form in the direction of the unit normal C(i), respectively. Suppose that the third fundamental form t satisfies dt(X, Y ) = 2��g(��X, Y ) for certain scalar ��(≠ 2c)and any vector fields X and Y and at the same time Rξ is ��∇ξξ-parallel, then M is a Hopf hypersurface in Mn(c) provided that it satisfies RξA(1) = A(1)Rξ, RξA(2) = A(2)Rξ and ${\bar{r}}-2(n-1)c{\leq}0$, where ${\bar{r}}$ denotes the scalar curvature of M.