Poincaré formulas of complex submanifolds

Poincaré formulas of complex submanifolds

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

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

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.

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Primary Subjects: 53C65

Keywords: Poincaré formula; complex submanifolds; almost Hermitian homogeneous spaces

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1116014787
Mathematical Reviews number (MathSciNet): MR2075452
Zentralblatt MATH identifier: 02138349
Digital Object Identifier: doi:10.3792/pjaa.80.110

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References

Howard, R.: The kinematic formula in Riemannian homogeneous spaces. Mem. Amer. Math. Soc., 106, no. 509 (1993).

Mathematical Reviews (MathSciNet): MR1169230

Sakai, T.: Poincaré formula in irreducible Hermitian symmetric spaces. Tokyo J. Math., 26 (2), 541--547 (2003).

Mathematical Reviews (MathSciNet): MR2020802

Santaló, L. A.: Integral geometry in Hermitian spaces. Amer. J. Math., 74, 423--434 (1952).

Mathematical Reviews (MathSciNet): MR48062

Tasaki, H.: Integral geometry under cut loci in compact symmetric spaces. Nagoya Math. J., 137, 33--53 (1995).

Mathematical Reviews (MathSciNet): MR1324543

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