Geodesic
The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor
Communications in Mathematics, Tome 21 (2013) no. 1, pp. 77-90

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By using the technique of decomposition of a Hermitian vector space under the action of a unitary group, Ganchev [2] obtained a tensor which he named the Weyl component of the antiholomorphic curvature tensor. We show that the same tensor can be obtained by direct application of the conformal change of the metric to the antiholomorphic curvature tensor. Also, we find some other conformally curvature tensors and examine some relations between them.
By using the technique of decomposition of a Hermitian vector space under the action of a unitary group, Ganchev [2] obtained a tensor which he named the Weyl component of the antiholomorphic curvature tensor. We show that the same tensor can be obtained by direct application of the conformal change of the metric to the antiholomorphic curvature tensor. Also, we find some other conformally curvature tensors and examine some relations between them.
Classification : 53C56
Keywords: almost Hermitian manifold; antiholomorphic curvature tensor; conformal change of metric 
Prvanović, Mileva. The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor. Communications in Mathematics, Tome 21 (2013) no. 1, pp. 77-90. http://geodesic.mathdoc.fr/item/COMIM_2013_21_1_a4/
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