Proceedings of the Japan Academy, Series A, Mathematical Sciences

Poincaré formulas of complex submanifolds

Hong Jae Kang, Takashi Sakai, Masaro Takahashi, and Hiroyuki Tasaki

Full-text: Open access


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.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 6 (2004), 110-112.

First available in Project Euclid: 13 May 2005

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]

Poincaré formula complex submanifolds almost Hermitian homogeneous spaces


Kang, Hong Jae; Sakai, Takashi; Takahashi, Masaro; Tasaki, Hiroyuki. Poincaré formulas of complex submanifolds. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 6, 110--112. doi:10.3792/pjaa.80.110.

Export citation


  • Howard, R.: The kinematic formula in Riemannian homogeneous spaces. Mem. Amer. Math. Soc., 106, no. 509 (1993).
  • Sakai, T.: Poincaré formula in irreducible Hermitian symmetric spaces. Tokyo J. Math., 26 (2), 541–547 (2003).
  • Santaló, L. A.: Integral geometry in Hermitian spaces. Amer. J. Math., 74, 423–434 (1952).
  • Tasaki, H.: Integral geometry under cut loci in compact symmetric spaces. Nagoya Math. J., 137, 33–53 (1995).