Curvature tensors on almost Hermitian manifolds

Tricerri, Franco; Vanhecke, Lieven

doi:10.1090/S0002-9947-1981-0626479-0

Curvature tensors on almost Hermitian manifolds
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by Franco Tricerri and Lieven Vanhecke PDF

Trans. Amer. Math. Soc. 267 (1981), 365-398 Request permission

Abstract:

A complete decomposition of the space of curvature tensors over a Hermitian vector space into irreducible factors under the action of the unitary group is given. The dimensions of the factors, the projections, their norms and the quadratic invariants of a curvature tensor are determined. Several applications for almost Hermitian manifolds are given. Conformal invariants are considered and a general Bochner curvature tensor is introduced and shown to be a conformal invariant. Finally curvature tensors on four-dimensional manifolds are studied in detail.

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