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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Kinematic formulas for Weyl's curvature invariants of submanifolds in complex projective space


Author: Tōru Ishihara
Journal: Proc. Amer. Math. Soc. 97 (1986), 483-487
MSC: Primary 53C65; Secondary 53C40, 53C55
DOI: https://doi.org/10.1090/S0002-9939-1986-0840634-6
MathSciNet review: 840634
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Abstract: It is shown in [5] that Weyl's curvature invariants $ {k_{2p}}(M)$ can be expressed by $ {\gamma _q} \wedge {F^{m - q}}[M]$, where $ M$ is a $ 2m$-dimensional Kähler submanifold with compact closure in a space of constant holomorphic curvature, $ {\gamma _q}$ is the $ q$th Chern form of $ M$ and $ F$ is the Kähler form of $ M$. In this paper, we shall show that each $ {\gamma _q} \wedge {F^{m - q}}[M]$ is expressible in terms of $ F$ and $ {k_{2p}}(M)$. Using this result, we get kinematic formulas for $ {k_{2p}}(M)$ from Shifrin's [8] kinematic formulas for Chern classes.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0840634-6
Keywords: Kinematic formulas, Chern forms, Weyl's curvature invariants
Article copyright: © Copyright 1986 American Mathematical Society