• Honam Mathematical Journal
• /
• v.46 no.4
• /
• pp.629-634
• /
• 2024

The W₅-curvature tensor has been studied in the space- time of general relativity. The space-time satisfying Einstein's field equations with cosmological term and vanishing W₅-curvature tensor has been considered and it has been shown that metric tensor is proportional to the energy-momentum tensor. The existence of Killing as well as conformal Killing vector fields have been shown. Further for a W₅-flat perfect fluid space-time satisfying Einstein's field equations, the isotropic pressure has been found to be the function of cosmological constant and non-zero gravitational constant.

• 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.