• Kyungpook Mathematical Journal
• /
• v.58 no.1
• /
• pp.149-165
• /
• 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
• /
• v.44 no.2
• /
• pp.179-194
• /
• 2022

In the present study, we investigate generic lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving the existence of generic lightlike submanifolds in an indefinite generalized complex space form, a non-trivial example of this class of submanifolds is discussed. Then, we find a characterization theorem enabling the induced connection on a generic lightlike submanifold to be a metric connection. We also derive some conditions for the integrability of distributions defined on generic lightlike submanifolds. Further, we discuss the non-existence of mixed geodesic generic lightlike submanifolds in a generalized complex space form. Finally, we investigate totally umbilical generic lightlike submanifolds and minimal generic lightlike submanifolds of an indefinite nearly Kaehler manifold.

• East Asian mathematical journal
• /
• v.24 no.4
• /
• pp.421-429
• /
• 2008

We study invariant lightlike submanifolds and almost contact CR-lightlike submanifolds of an indefinite cosymplectic manifold.

• Honam Mathematical Journal
• /
• v.42 no.1
• /
• pp.123-137
• /
• 2020

The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian space-forms. We deduce some results related to the invariant and anti-invariant slant submanifolds of the generalized Sasakian spaceforms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical submanifolds of the generalized Sasakian space-forms. To prove the existence of almost semiinvariant and anti-invariant submanifolds, we provide the non-trivial examples.

• Honam Mathematical Journal
• /
• v.43 no.2
• /
• pp.239-258
• /
• 2021

In the present paper, we introduce the study of slant lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving some geometric results for the existence of slant lightlike submanifolds of indefinite nearly Kaehler manifolds, we give a non-trivial example of this class of lightlike submanifolds. Then, we derive some conditions for the integrability of the distributions associated with slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Consequently, we study totally umbilical slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Subsequently, we investigate minimal slant lightlike submanifolds of indefinite nearly Kaehler manifolds.

• Communications of the Korean Mathematical Society
• /
• v.22 no.1
• /
• pp.123-135
• /
• 2007

This paper has two objectives. The first objective is to study slant submanifolds of quaternion Kaehler manifolds. We give characterization theorems and examples of slant submanifolds. For the second objective, we introduce the notion of semi-slant submanifolds which are different from the definition of N. Papaghiuc [15]. We obtain characterization theorems, examples of semi-slant sub manifolds and investigate the geometry of leaves of distributions which are involved in the definition of semi-slant submanifolds.

• The Pure and Applied Mathematics
• /
• v.20 no.2
• /
• pp.89-101
• /
• 2013

In this paper, we study half lightlike submanifolds M of an indefinite cosymplectic manifold $\bar{M}$, whose structure vector field is not tangent to M. First, we construct two types of such half lightlike submanifolds, named by transversal and normal half lightlike submanifolds. Next, we characterize the lightlike geometries of such two types half lightlike submanifolds.

• Communications of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.935-949
• /
• 2019

The purpose of the paper is to study the notion of pseudo-slant submanifolds and the existence of some structures on a pseudo-slant submanifolds of nearly (${\varepsilon},{\delta}$)-trans-Sasakian manifold. Totally umbilical proper-slant submanifolds are worked out. We discuss the integrability of distributions on pseudo-slant submanifolds of nearly (${\varepsilon},{\delta}$)-trans-Sasakian manifold.

• Honam Mathematical Journal
• /
• v.44 no.1
• /
• pp.1-16
• /
• 2022

In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.437-452
• /
• 1997

We study low type submanifolds in pseudo-Euclidean space which is especially of 2-type pseudo-umbilical. We also determine full null 2-type surfaces with parallel mean curvature vector in 4-dimensional Minkowski space-time.