• 대한수학회논문집
• /
• 제34권4호
• /
• pp.1303-1313
• /
• 2019

Recently Hui et al. ([8,9]) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. The characterization for both these classes of warped product submanifolds have been studied here. It is also shown that there do not exists any proper warped product bi-slant submanifold of a $(LCS)_n$-manifold. Although the existence of a bi-slant submanifold of $(LCS)_n$-manifold is ensured by an example.

• 통합자연과학논문집
• /
• 제5권1호
• /
• pp.42-45
• /
• 2012

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on Riemannian warped product manifold $M=({\alpha},\;{\infty}){\times}_fN$ with prescribed scalar curvature functions.

• 대한수학회보
• /
• 제41권4호
• /
• pp.691-697
• /
• 2004

In this paper we find index form of the multiply warped product manifolds to investigate the physical properties from space-time.

• 대한수학회논문집
• /
• 제25권4호
• /
• pp.615-621
• /
• 2010

We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. If M is $(PS)_n$, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is $(PRS)_n$, then we show that (i) N is Ricci symmetric and (ii) M is $(PRS)_n$ if and only if the tensor T defined by (2.6) satisfies a certain condition.

• 대한수학회지
• /
• 제47권3호
• /
• pp.505-521
• /
• 2010

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

• 대한수학회보
• /
• 제37권2호
• /
• pp.317-336
• /
• 2000

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future (or past) complete Lorentzian metrics on $M=(-{\infty},{\;}\infty){\;}{\times}f^N$ with specific scalar curvatures.

• 대한수학회지
• /
• 제43권1호
• /
• pp.133-145
• /
• 2006

We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p{\in}M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of TpM, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제4권1호
• /
• pp.27-33
• /
• 1997

Let (M = B$\times$f F, g) be an ($n \geq3$ )-dimensional differential manifold with Riemannian metric g. We solve the following elliptic nonlinear partial differential equation (equation omitted). where $\Delta_{g}$ is the Laplacian in the $\Delta$g-metric and ($h(\chi)$) is the scalar curvature of g and ($H(\chi)$) is a function on M.

• 대한수학회지
• /
• 제28권1호
• /
• pp.23-35
• /
• 1991

• Kyungpook Mathematical Journal
• /
• 제46권3호
• /
• pp.367-376
• /
• 2006

We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.