• Kyungpook Mathematical Journal
• /
• 제49권4호
• /
• pp.789-799
• /
• 2009

In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.

• 대한수학회논문집
• /
• 제35권2호
• /
• pp.603-611
• /
• 2020

The purpose of this note is to introduce a type of Riemannian manifold called an almost quasi Ricci symmetric manifold and investigate the several properties of such a manifold on which some geometric conditions are imposed. And the existence of such a manifold is ensured by a proper example.

• Kyungpook Mathematical Journal
• /
• 제45권1호
• /
• pp.95-103
• /
• 2005

The present paper deals with Lorentzian ${\alpha}-Sasakian$ manifolds with conformally flat and quasi conform ally flat curvature tensor. It is shown that in both cases, the manifold is locally isometric with a sphere $S^{2^{n}+1}(c)$. Further it is shown that an Lorentzian ${\alpha}-Sasakian$ manifold with R(X, Y).C = 0 is locally isometric with a sphere $S^{2^{n}+1}(c)$, where c = ${\alpha}^2$.

• 대한수학회지
• /
• 제57권2호
• /
• pp.539-552
• /
• 2020

In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.

• 대한수학회보
• /
• 제38권1호
• /
• pp.157-161
• /
• 2001

In this paper, we prove that an affine manifold M is finitely covered by a manifold $\overline{M}$ where $\overline{M}$ is radiant or the tangent bundle of $\overline{M}$ has a conformally flat vector subbundle of the projective holonomy group of M admits an invariant probability Borel measure. This implies that$x^M$is zero.

• Kyungpook Mathematical Journal
• /
• 제55권3호
• /
• pp.731-739
• /
• 2015

The object of the present paper is to characterize a Riemannian manifold admitting a type of semi-symmetric non-metric connection.

• Kyungpook Mathematical Journal
• /
• 제60권4호
• /
• pp.821-830
• /
• 2020

The object of the present paper is to classify a special type of spacetime, called Lorentzian para-Sasakian type spacetime (4-dimensional LP-Sasakian manifold with a coefficient α) satisfying certain curvature conditions.

• 대한수학회보
• /
• 제60권3호
• /
• pp.705-715
• /
• 2023

In this paper, we present some new properties for p-biharmonic hypersurfaces in a Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces. We present some open problems.

• Kyungpook Mathematical Journal
• /
• 제60권3호
• /
• pp.571-584
• /
• 2020

The object of the present paper is to characterize generalized Ricci recurrent (GR₄) spacetimes. Among others things, it is proved that a conformally flat GR₄ spacetime is a perfect fluid spacetime. We also prove that a GR₄ spacetime with a Codazzi type Ricci tensor is a generalized Robertson Walker spacetime with Einstein fiber. We further show that in a GR₄ spacetime with constant scalar curvature the energy momentum tensor is semisymmetric. Further, we obtain several corollaries. Finally, we cite some examples which are sufficient to demonstrate that the GR₄ spacetime is non-empty and a GR₄ spacetime is not a trivial case.

• 대한수학회논문집
• /
• 제24권3호
• /
• pp.415-424
• /
• 2009

The object of the present paper is to study the generalized quasi-Einstein manifolds satisfying some conditions. Finally the existence of such manifolds is ensured by several interesting examples.