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

Abstract:

It is shown in [5] that Weyl’s curvature invariants ${k_{2p}}(M)$ 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.