# ON $\eta$K-CONFORMAL KILLING TENSOR IN COSYMPLECTIC MANIFOLD WITH VANISHING COSYMPLECTIC BOCHNER CURVATURE TENSOR$^*$

• Jun, Jae-Bok (Department of Mathematics Educations, kookmin University , Seoul 136-702) ;
• Kim, Un-Kyu (Department of Mathematics Educations, Sung Yun Kwan University, Seoul 110-745)
• Published : 1995.02.01

#### Abstract

S. Tachibana [10] has defined a confornal Killing tensor in a n-dimensional Riemannian manifold M by a skew symmetric tensor $u_[ji}$ satisfying the equation $$\nabla_k u_{ji} + \nabla_j u_{ki} = 2\rho_i g_{kj} - \rho_j g_{ki} - \rho_k g_{ji},$$ where $g_{ji}$ is the metric tensor of M, $\nabla$ denotes the covariant derivative with respect to $g_{ji}$ and $\rho_i$ is a associated covector field of $u_{ji}$. In here, a covector field means a 1-form.