Pseudo-Chern classes of an almost pseudo-Hermitian manifold

Matsushita, Yasuo

doi:10.1090/S0002-9947-1987-0882709-7

Pseudo-Chern classes of an almost pseudo-Hermitian manifold
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by Yasuo Matsushita

Trans. Amer. Math. Soc. 301 (1987), 665-677

DOI: https://doi.org/10.1090/S0002-9947-1987-0882709-7

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Abstract:

For an almost pseudo-Hermitian manifold, pseudo-Chern classes are defined on its complexified tangent bundle with the pseudo-Hermitian structure as represented by certain ${\text {ad}}(U(p, q))$-invariant forms on the manifold. It is shown that such a manifold always admits an almost Hermitian structure, and hence that Chern classes are also defined on the complexified tangent bundle with such an almost Hermitian structure. A relation between the pseudo-Chern classes and the Chern classes is established. From the relation, the pseudo-Chern classes are considered as the characteristic classes which measure how the almost pseudo-Hermitian structure deviates from an almost Hermitian structure.

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