Asian Journal of Mathematics

Volume 23 (2019)

Number 3

Isometries of extrinsic symmetric spaces

Pages: 439 – 454



J.-H. Eschenburg (Institut für Mathematik, Universität Augsburg, Germany )

P. Quast (Institut für Mathematik, Universität Augsburg, Germany)

M. S. Tanaka (Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, Japan)


We show that every isometry of an extrinsic symmetric space extends to an isometry of its ambient euclidean space. As a consequence, any isometry of a real form of a hermitian symmetric space extends to a holomorphic isometry of the ambient hermitian symmetric space. Moreover, every fixed point component of an isometry of a symmetric $R$-space is a symmetric $R$-space itself.


extrinsic symmetric spaces, isometries

2010 Mathematics Subject Classification

53C35, 53C40

Received 29 July 2016

Accepted 6 February 2018

Published 9 July 2019