## On symmetric Cauchy-Riemann manifolds

#####
**Citation: **

*Kaup, Wilhelm; Zaitsev, Dmitri 'On symmetric Cauchy-Riemann manifolds' in Advances in Mathematics, 149, (2), 2000, pp 145 - 181*

#####
**Download Item: **

On symmetric.pdf (published (author copy) peer-reviewed) 341.8Kb

#####
**Abstract: **

The Riemannian symmetric spaces play an important role in different branches of mathematics.
By definition, a (connected) Riemannian manifold M is called symmetric if, to every
a ? M, there exists an involutory isometric diffeomorphism sa:M ? M having a as isolated
fixed point in M (or equivalently, if the differential dasa is the negative identity on the the
tangent space Ta = TaM of M at a). In case such a transformation sa exists for a ? M, it is
uniquely determined and is the geodesic reflection of M about the point a. As a consequence,
for every Riemannian symmetric space M, the group G = GM generated by all symmetries sa,
a ? M, is a Lie group acting transitively on M. In particular, M can be identified with the
homogeneous space G/K for some compact subgroup K ? G. Using the elaborate theory of Lie
groups and Lie algebras E.Cartan classified all Riemannian symmetric spaces.

#####
**Author's Homepage: **

http://people.tcd.ie/zaitsevd
#####
**Description: **

PUBLISHED
**Author:**ZAITSEV, DMITRI

#####
**Publisher: **

Elsevier
#####
**Type of material: **

Journal Article#####
**Series/Report no: **

Advances in Mathematics149

2

#####
**Availability: **

Full text available#####
**Keywords: **

Pure & Applied Mathematics
Licences: