• 대한수학회보
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• 제49권4호
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• pp.863-874
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• 2012

We provide a study of lightlike hypersurfaces of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike hypersurfaces with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.

• 대한수학회보
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• 제46권3호
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• pp.401-408
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• 2009

The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient $\alpha$. Among others it is shown that if an LP-Sasakian manifold with a coefficient $\alpha$ is a manifold of constant curvature, then the manifold is the product manifold. Also it is proved that a 3-dimensional Ricci semisymmetric LP-Sasakian manifold with a constant coefficient $\alpha$ is a spaceform.

• 대한수학회논문집
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• 제35권1호
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• pp.269-278
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• 2020

This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η-Einstein manifold were determined.

• 대한수학회지
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• 제39권5호
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• pp.693-708
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• 2002

The warped product L$\times$$_{f}$ F of a line L and a Kaehler manifold F is a typical example of Kenmotsu manifold. In this paper we determine submanifolds of L$\times$$_{f}$ F which are tangent to the structure vector field and satisfy certain conditions concerning with Ricci curvature and mean curvature.ure.

• 대한수학회보
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• 제54권2호
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• pp.399-416
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• 2017

In this paper, we study a class of Finsler metrics called general (${\alpha},{\beta}$)-metrics, which are defined by a Riemannian metric ${\alpha}$ and a 1-form ${\beta}$. We show that every general (${\alpha},{\beta}$)-metric with isotropic Berwald curvature is either a Berwald metric or a Randers metric. Moreover, a lot of new isotropic Berwald general (${\alpha},{\beta}$)-metrics are constructed explicitly.

• 대한수학회보
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• 제57권4호
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• pp.1049-1060
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• 2020

We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in [26] and we also remove the condition that the second fundamental form is uniformly bounded when t ∈ (-∞, -1).

• 대한수학회보
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• 제29권1호
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• pp.25-29
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• 1992

The purpose of this paper is to study indefinite Kaehlerian metrics with vanishing conformal curvature tensor field. In the first section, a brief summary of the complex version of indefinite Kaehlerian manifolds is recalled and we introduce the conformal curvature tensor field on an indefinite Kaehlerian manifold. In section 2, we obtain the theorem for indefinite Kaehlerian metrics with vanishing conformal curvature tensor field.

• 대한수학회지
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• 제34권2호
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• pp.321-336
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• 1997

Let S be the Ricci curvature of an n-dimensional compact minimal totally real submanifold M of a quaternion projective space $HP^n (c)$ of quaternion sectional curvature c. We proved that if $S \leq \frac{16}{3(n -2)}c$, then either $S \equiv \frac{4}{n - 1}c$ (i.e. M is totally geodesic or $S \equiv \frac{16}{3(n - 2)}c$. All compact minimal totally real submanifolds of $HP^n (c)$ satisfy in $S \equiv \frac{16}{3(n - 2)}c$ are determined.

• 대한수학회보
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• 제50권3호
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• pp.867-871
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• 2013

It has been conjectured that, on a compact 3-dimensional orientable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker $s^{\prime}^*_g{\neq}0$, which generalizes the previous partial results.

• 대한수학회보
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• 제50권5호
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• pp.1567-1586
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• 2013

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connection and generalized Kasner spacetimes with a semi-symmetric non-metric connection and find some new examples of Einstein affine manifolds and affine manifolds with constant scalar curvature. We also consider the multiply warped products with an affine connection with a zero torsion.