This article is cited in 6 papers

Geometry of the Conharmonic Curvature Tensor of Almost Hermitian Manifolds

V. F. Kirichenko^a, A. R. Rustanov^a, A. A. Shikhab

^a Moscow State Pedagogical University

Abstract: We obtain a criterion for manifolds of dimension $4$ and greater to be conharmonically para-Kähler and the condition for a manifold to be conharmonically flat.

Keywords: almost Hermitian manifold, Riemannian structure, conharmonic curvature tensor, Kähler manifold, para-Kähler manifold, Riemannian metric, nearly Kähler structure, $G$-structure, Riemannian curvature, Ricci tensor.

UDC: 514.764.21

Received: 22.07.2009

DOI: 10.4213/mzm8625

 English version: Mathematical Notes, 2011, 90:1, 79–93

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