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.
Citation
Antonio Lotta. "On model mutation for reductive Cartan geometries and non-existence of Cartan space forms." Kodai Math. J. 27 (2) 174 - 188, June 2004. https://doi.org/10.2996/kmj/1093351324
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