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

Salimov, A. A.

Tr. Geom. Semin. 16, 91-103 (1984).

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.Mikeš

MSC:

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

Keywords:

affine connection; polyaffine structure; holomorphic-projective transformations