Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 32 Issue 1
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- Pages.25-34
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- 1995
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
ON $\eta$ K-CONFORMAL KILLING TENSOR IN COSYMPLECTIC MANIFOLD WITH VANISHING COSYMPLECTIC BOCHNER CURVATURE TENSOR$^*$
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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.
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