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Keywords:
almost Hermitian manifold; antiholomorphic curvature tensor; conformal change of metric
almost Hermitian manifold; antiholomorphic curvature tensor; conformal change of metric
Summary:
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.
References:
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[2] Ganchev, G.: Bochner curvature tensors in almost Hermitian manifolds. PLISKA, Stud. Math. Bulg., 9, 1987, 33-43, MR 0892678 | Zbl 0622.53013
[3] Mikeš, J., Kiosak, V., Vanžurová, A.: Geodesic Mappings of Manifolds with Affine Connection. 2008, Palacký University, Faculty of Science, Olomouc, MR 2488821 | Zbl 1176.53004
[4] Prvanović, M.: On the cutvature tensor of Kähler type in an almost Hermitian and almost anti-Hermitian manifolds. Mat. Vasnik, 50, 1998, 57-64, MR 1640886
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[7] Tricerrri, F., Vanhecke, L.: Curvature tensors on almost Hermitian manifolds. Trans. Amer. Math. Soc., 267, 1981, 365-398, DOI 10.1090/S0002-9947-1981-0626479-0 | MR 0626479
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