We formulate Poincaré formulas of complex submanifolds in almost Hermitian homogeneous spaces, using Howard's formulation of Poincaré formulas in Riemannian homogeneous spaces. This formula is an extension of Santaló's one in complex space forms.
"Poincaré formulas of complex submanifolds." Proc. Japan Acad. Ser. A Math. Sci. 80 (6) 110 - 112, June 2004. https://doi.org/10.3792/pjaa.80.110