## Kodai Mathematical Journal

### On model mutation for reductive Cartan geometries and non-existence of Cartan space forms

Antonio Lotta

#### Abstract

Reductive models $((\frak g,\frak h),H)$ for Cartan geometries are showed to fall into two classes, symmetric and non symmetric type, according to the existence or non existence of a mutation $\frak g'=\frak h\oplus\frak m$ where the $H$-module $\frak m$ is an abelian subalgebra. Sasakian structures are showed to be Cartan geometries having a model of non symmetric type and other examples of models of this type are exhibited. Reductive models for which no Cartan space forms exist are constructed. The phenomenon of non-existence of Cartan space forms pertains to models of non symmetric type.

#### Article information

Source
Kodai Math. J., Volume 27, Number 2 (2004), 174-188.

Dates
First available in Project Euclid: 24 August 2004

https://projecteuclid.org/euclid.kmj/1093351324

Digital Object Identifier
doi:10.2996/kmj/1093351324

Mathematical Reviews number (MathSciNet)
MR2069768

Zentralblatt MATH identifier
1078.53041

#### Citation

Lotta, Antonio. On model mutation for reductive Cartan geometries and non-existence of Cartan space forms. Kodai Math. J. 27 (2004), no. 2, 174--188. doi:10.2996/kmj/1093351324. https://projecteuclid.org/euclid.kmj/1093351324