Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
On model mutation for reductive Cartan geometries and non-existence of Cartan space forms
Antonio Lotta
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2004 年 27 巻 2 号 p. 174-188

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Reductive models ((\mathfrak{g}, \mathfrak{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 \mathfrak{g}'=\mathfrak{h}⊕\mathfrak{m} where the H-module 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.
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© Department of Mathematics, Tokyo Institute of Technology
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