대한수학회보 (Bulletin of the Korean Mathematical Society)
- 제33권3호
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- Pages.455-463
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- 1996
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
Conformally invariant tensors on hermitian manifolds
- Matsuo, Koji (Department of Mathematics, Ichinoseki National Collegee of Technology)
- 발행 : 1996.08.01
초록
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.