Abstract
It is shown in [5] that Weyl’s curvature invariants k 2 p ( M ) {k_{2p}}(M) can be expressed by γ q ∧ F m − q [ M ] {\gamma _q} \wedge {F^{m - q}}[M] , where M M is a 2 m 2m -dimensional Kähler submanifold with compact closure in a space of constant holomorphic curvature, γ q {\gamma _q} is the q q th Chern form of M M and F F is the Kähler form of M M . In this paper, we shall show that each γ q ∧ F m − q [ M ] {\gamma _q} \wedge {F^{m - q}}[M] is expressible in terms of F F and k 2 p ( M ) {k_{2p}}(M) . Using this result, we get kinematic formulas for k 2 p ( M ) {k_{2p}}(M) from Shifrin’s [8] kinematic formulas for Chern classes.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.