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• W2408966051 abstract "The theory developed for certain geometric structures (the so-called parabolic geometries) was successfully applied in a study of functions of sev- eral quaternionic variables satisfying the Fueter (Dirac) equation in each vari- able separately. The special case of a parabolic geometry used in this applica- tion is the quaternionic structure on a manifold with dimension 4n. A homo- geneous model for quaternionic geometry is the quaternionic projective space P n (H). A question discussed in the paper is whether similar applications are possible for dimensions different from four. In the quaternionic case, the Dirac operator is acting on functions de- fined on R 4n , considered as an open dense subset in P n (H). This situation has no natural generalization in dimensions different from four. In the paper, we are discussing a possibility to embed R 4n to a homogeneous model for another type of a parabolic geometry in such a way that it would admit gen- eralizations to higher dimensions. There is, indeed, another possibility with such a property but there is a price to pay for it. The embedding is no more onto an open dense subset, there are 'dummy' variables necessarily present. It is possible to show that a suitable invariant first order differential operator in the corresponding parabolic geometry, when acting on functions indepen- dent of those dummy variables, coincides with the Fueter operators in several quaternionic variables. This scheme can be extended also to other dimensions, different from four." @default.
• W2408966051 created "2016-06-24" @default.
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• W2408966051 date "2008-01-01" @default.
• W2408966051 modified "2023-09-24" @default.
• W2408966051 title "Parabolic Geometries Related with Several" @default.
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