Proceedings of the Japan Academy, Series A, Mathematical Sciences

Poincaré formulas of complex submanifolds

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

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Abstract

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

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

Dates
First available in Project Euclid: 13 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116014787

Digital Object Identifier
doi:10.3792/pjaa.80.110

Mathematical Reviews number (MathSciNet)
MR2075452

Zentralblatt MATH identifier
1073.53100

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

Keywords
Poincaré formula complex submanifolds almost Hermitian homogeneous spaces

Citation

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. https://projecteuclid.org/euclid.pja/1116014787


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References

  • 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).