• Journal of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.129-167
• /
• 2003

In this paper we introduce new notions of Ricci-like tensor and many kind of curvature-like tensors such that concircular, projective, or conformal curvature-like tensors defined on semi-Riemannian manifolds. Moreover, we give some geometric conditions which are equivalent to the Codazzi tensor, the Weyl tensor, or the second Bianchi identity concerned with such kind of curvature-like tensors respectively and also give a generalization of Weyl's Theorem given in [18] and [19].

• Honam Mathematical Journal
• /
• v.36 no.4
• /
• pp.795-803
• /
• 2014

In this paper, we decompose the curvature tensor (field) on the Abbena-Thurston manifold into three curvature-like tensor fields, and investigate geometric properties.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.81-99
• /
• 2006

We investigate a curvature-like tensor defined by (3.1) in Sasakian manifold of $dimension{\geq}$ 5, and show that this tensor satisfies some properties. Especially, we determine compact Sasakian manifolds with vanishing this tensor and improve some theorems concerning contact conformal curvature tensor and spectrum of Laplacian acting on $p(0{\leq}P{\leq}2)-forms$ on the manifold by using this tensor component.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.229-241
• /
• 2015

In this paper, we decompose the curvature tensor (field) on the homogeneous Riemannian manifold SU(3)=T (k, l) with an arbitrarily given SU(3)-invariant Riemannian metric into three curvature-like tensor fields, and investigate geometric properties.

• Honam Mathematical Journal
• /
• v.45 no.2
• /
• pp.316-324
• /
• 2023

The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P_𝛼𝛽. It is established that the divergence of tensor G_𝛼𝛽 defined with the help of P_𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V₄ satisfying Einstein like field equations, the tensor P_𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.455-463
• /
• 1996

In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

• Honam Mathematical Journal
• /
• v.41 no.4
• /
• pp.669-682
• /
• 2019

The objective of this paper is to introduce and study Einstein-like para-Kenmotsu manifolds. For a para-Kenmotsu manifold to be Einstein-like, a necessary and sufficient condition in terms of its curvature tensor is obtained. We also obtain the scalar curvature of an Einstein-like para-Kenmotsu manifold. A necessary and sufficient condition for an almost para-contact metric hypersurface of a locally product Riemannian manifold to be para-Kenmotsu is derived and it is shown that the para-Kenmotsu hypersurface of a locally product Riemannian manifold of almost constant curvature is always Einstein.

• Bulletin of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.231-241
• /
• 1991

Recently, many mathematicians([NT], [Ka], [TV], [CW], etc.) studied foliated structures on a smooth manifold with the viewpoint of transversal differential geometry. In this paper, we shall discuss certain hermitian foliations F on a riemannian manifold with a bundle-like metric, that is, their transversal bundles to F have hermitian structures.

• Communications of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.331-343
• /
• 2014

The object of the present paper is to study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold. In this paper, we study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold whose projective curvature tensor satisfies certain curvature conditions.