zbMATH — the first resource for mathematics

On almost complex geoodular manifolds. (Russian) Zbl 0637.53052
Webs and quasigroups, Interuniv. thematic Collect. sci. Works, Kalinin 1987, 4-9 (1987).
[For the entire collection see Zbl 0611.00007.]
The subject of this paper is devoted to further investigation of relations between the objects of nonassociative algebra and differential geometry. For a detailed interpretation of these ideas and some main results see the fundamental work of L. V. Sabinin [Methods of nonassociative algebra in differential geometry. Addition to S. Kobayashi and K. Nomizu, Foundation of differential geometry V. I (Russian) (Nauka, Moskva 1981; Zbl 0526.53001)].
In this paper smooth local left geoodular manifolds over the field of complex numbers are considered. A generalization of these objects is introduced, being called almost complex geoodular manifold. A one-one correspondence between almost complex geoodular manifolds and almost complex manifolds with almost complex linear connection is established.
Reviewer: M.Malakhal’tsev

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
17D99 Other nonassociative rings and algebras