We describe the Poincar\'e formula for two complex submanifolds in irreducible Hermitian symmetric spaces. That can be expressed as a constant times the product of the volumes of two submanifolds under some conditions.
"Poincar\'e Formula in Irreducible Hermitian Symmetric Spaces." Tokyo J. Math. 26 (2) 541 - 547, December 2003. https://doi.org/10.3836/tjm/1244208607