• 대한수학회논문집
• /
• 제29권2호
• /
• pp.295-310
• /
• 2014

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

• 대한수학회보
• /
• 제49권4호
• /
• pp.863-874
• /
• 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.

• 대한수학회지
• /
• 제34권2호
• /
• pp.321-336
• /
• 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.

• Kyungpook Mathematical Journal
• /
• 제58권2호
• /
• pp.389-398
• /
• 2018

In this paper we obtain the condition for the existence of Ricci solitons in nonflat quaternion space form by using Eisenhart problem. Also it is proved that if (g, V, ${\lambda}$) is Ricci soliton then V is solenoidal if and only if it is shrinking, steady and expanding depending upon the sign of scalar curvature. Further it is shown that Ricci soliton in semi-symmetric quaternion space form depends on quaternion sectional curvature c if V is solenoidal.

• 대한수학회지
• /
• 제49권5호
• /
• pp.977-991
• /
• 2012

Let (M,F) and (M',F') be two foliated Riemannian manifolds with M compact. If the transversal Ricci curvature of F is nonnegative and the transversal sectional curvature of F' is nonpositive, then any transversally harmonic map ${\phi}:(M,F){\rightarrow}(M^{\prime},F^{\prime})$ is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then ${\phi}$ is transversally constant.

• 대한수학회논문집
• /
• 제22권3호
• /
• pp.411-417
• /
• 2007

N(k)-quasi Einstein manifolds are introduced and studied.

• Kyungpook Mathematical Journal
• /
• 제59권1호
• /
• pp.163-174
• /
• 2019

The object of this paper is to classify paracontact metric ($k,{\mu}$)-spaces satisfying certain curvature conditions. We show that a paracontact metric ($k,{\mu}$)-space is Ricci semisymmetric if and only if the metric is Einstein, provided k < -1. Also we prove that a paracontact metric ($k,{\mu}$)-space is ${\phi}$-Ricci symmetric if and only if the metric is Einstein, provided $k{\neq}0$, -1. Moreover, we show that in a paracontact metric ($k,{\mu}$)-space with k < -1, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. Several consequences of these results are discussed.

• 충청수학회지
• /
• 제33권2호
• /
• pp.219-226
• /
• 2020

In this paper, we consider gradient Ricci solitons and gradient Yamabe solitons in the warped product spaces. Also we study warped product space with harmonic curvature related to gradient Ricci solitons and gradient Yamabe solitons. Consequently some theorems are generalized and we derive differential equations for a warped product space to be a gradient Ricci soliton.

• 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.

• 호남수학학술지
• /
• 제40권3호
• /
• pp.447-456
• /
• 2018

In this paper, we consider nonconstant warping functions on Einstein Lorentzian warped product manifolds $M=B{\times}_{f^2}F$ with an 1-dimensional base B which has a negative definite metric. As the results, we discuss that on M the resulting Einstein Lorentzian warped product metric is a future (or past) geodesically complete one outside a compact set.