AUTOMORPHISMS IN CONTACT-AFFINE STRUCTURES

Tyapin Nikita Aleksandrovich, Candidate of physical and mathematical sciences, associate professor, sub-department of geometry and mathematical analysis, Penza State University (40 Krasnaya street, Penza, Russia), kaf_geom@pnzgu.ru

514.76

Background. Contactaffine structure is a special case of the contact structure, particularly, it is a contact structure supplemeted by linear connectivity coordinated with the structure. In the article the coordination is considered as the invariance of contact distribution relative to parallel transfers in structure connectivity along any curves. The study of automorphisms of contact-affine structures is of interest due to the fact that the dimensionalities of these groups are trivially finite.
Materials and methods. To research the groups of automorphisms of contact-affine structures the author uses the methods of tensor analysis as well as the methods of Lie group theory and Lie algebra.
Results. The researcher discovered analytical conditions of coordination of the linear connectivity and the contact structure in the sense of invariance of the contact distribution relative to parallel transfers in the said linear connectivity along any curves. It is proved that in this case the structure connectivity necessarily has twisting. The article adduces the value from the top of the dimensionality of the group of automorphisms of the contact-affine structure.
Conclusions. The methods of tensor analysis as well as the methods of Lie group theory and Lie algeba allow effective researching of the groups of automorphisms of contact-affine structures.

contact structure, contact-affine structure, automorphisms of differential-geometric structures.

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