Holomorphic-projective transformations of connections on manifolds with structures defined by algebras. (Russian) Zbl 0607.53010

For spaces with a symmetric affine connection having an integrable polyaffine structure determining an n-regular presentation of an associative commutative unitary algebra, an analog to the well-known theory of holomorphic-projective transformations of complex manifolds, i.e. transformations preserving hypercomplex geodesics, is constructed. A class of manifolds admitting holomorphic-projective transformations into a flat space is distinguished, a tensorial condition for such spaces is obtained. Infinitesimal holomorphic-projective transformations, preserving a polyaffine structure are studied.
Reviewer: J.MikeŇ°


53B05 Linear and affine connections
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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