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The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor

Mileva Prvanović (2013)

Communications in Mathematics

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.

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