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

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.