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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Geometry associated with semisimple flat homogeneous spaces


Author: Takushiro Ochiai
Journal: Trans. Amer. Math. Soc. 152 (1970), 159-193
MSC: Primary 53.52
DOI: https://doi.org/10.1090/S0002-9947-1970-0284936-6
MathSciNet review: 0284936
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Abstract: Our object is Cartan connections with semisimple flat homogeneous spaces as standard spaces. We study these from the viewpoint of $ G$-structures of second order. This allows us especially to treat classical projective and conformal connections in the unifying manner. We also consider its application to the problem of certain geometric transformations.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0284936-6
Keywords: Graded Lie algebra, Spencer cohomology, semisimple Lie algebra, harmonic class, semisimple flat homogeneous space, bundle of higher order contact, linear connection, Cartan connection, normal Cartan connection, Weyl tensor
Article copyright: © Copyright 1970 American Mathematical Society