Tsukuba Journal of Mathematics

Simpleness and closedness of circles in compact Hermitian symmetric spaces

Toshiaki Adachi, Sadahiro Maeda, and Seiichi Udagawa

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Abstract

We first interpret circles in Riemannian Symmetric space by Lie algebro-theoretic formalism. In particular, it is a solution of the system of ordinary differential equation of first order. We divide circles into 3-types. We investigate closedness and simpleness for such circles in compact Hermitian symmetric spaces. Consequently, we find many open holomorphic circles and non-simple circles. Note that there exist no non-simple circles and no open holomorphic circles in compact Riemannian symmetric space of rank one.

Article information

Source
Tsukuba J. Math., Volume 24, Number 1 (2000), 1-13.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496164041

Digital Object Identifier
doi:10.21099/tkbjm/1496164041

Mathematical Reviews number (MathSciNet)
MR1791326

Zentralblatt MATH identifier
0997.53039

Citation

Adachi, Toshiaki; Maeda, Sadahiro; Udagawa, Seiichi. Simpleness and closedness of circles in compact Hermitian symmetric spaces. Tsukuba J. Math. 24 (2000), no. 1, 1--13. doi:10.21099/tkbjm/1496164041. https://projecteuclid.org/euclid.tkbjm/1496164041


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