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Curvature tensors on almost Hermitian manifolds


Authors: Franco Tricerri and Lieven Vanhecke
Journal: Trans. Amer. Math. Soc. 267 (1981), 365-398
MSC: Primary 53C15; Secondary 53C55
DOI: https://doi.org/10.1090/S0002-9947-1981-0626479-0
MathSciNet review: 626479
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0626479-0
Keywords: Curvature tensors, decomposition into irreducible components, unitary group, quadratic invariants, almost Hermitian manifolds, conformal invariants, Weyl tensor, Bochner tensor, four-dimensional manifolds, submanifolds
Article copyright: © Copyright 1981 American Mathematical Society

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