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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Pseudo-Chern classes of an almost pseudo-Hermitian manifold


Author: Yasuo Matsushita
Journal: Trans. Amer. Math. Soc. 301 (1987), 665-677
MSC: Primary 53C55; Secondary 53C50, 57R20
MathSciNet review: 882709
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0882709-7
PII: S 0002-9947(1987)0882709-7
Article copyright: © Copyright 1987 American Mathematical Society