• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.717-732
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• 2006

In this paper, we study both slant 3nd semi-slant sub-manifolds of an almost product Riemannian manifold. We give characterization theorems for slant and semi-slant submanifolds and investigate special class of slant submanifolds which are product version of Kaehlerian slant submanifold. We also obtain integrability conditions for the distributions which are involved in the definition of a semi-slant submanifold. Finally, we prove a theorem on the geometry of leaves of distributions under a condition.

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

• Honam Mathematical Journal
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• v.42 no.1
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• pp.151-160
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• 2020

In this paper, we obtain some necessary and sufficient conditions such that a semi-slant submanifold in a locally product Riemannian manifold reduces to a warped product semi-slant submanifold and also give an example supported this characterization.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.667-676
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• 2014

In this article, we study slant and semi-slant submanifolds of $(LCS)_n$-manifolds. Integrability conditions of distributions involved in definition of semi-slant submanifolds of a $(LCS)_n$-manifold have been obtained.

• 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.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.197-210
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• 2020

In this paper, we prove that there are no non-trivial 𝒫ℛ-semi-slant warped product submanifolds with proper slant coefficients in para-Kähler manifolds ${\bar{M}}$. We also present a numerical example that illustrates the existence of a 𝒫ℛ-warped product submanifold in ${\bar{M}}$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.979-998
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• 2009

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, $\theta$-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant $\Theta_k$ of different kind of submanifolds of a S-space form $\tilde{M}(c)$ are obtained.

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