• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site
Student
Title
Supervisor
Faculty
Educational Programme
Pavel Osipov
Flat Affine Manifolds
Mathematics
(Master’s programme)
2018
The Hessian geometry is the real analogue of the Kähler one. Sasakian geometry is an odd-dimensional counterpart of the Kähler geometry. In the paper, we study the connection between projective Hessian and Sasakian manifolds analogous to the one between Hessian and Kähler manifolds. In particular, we construct a Sasakian structure on $TM\times \R$ from a projective Hessian structure on $M$. Especially, we are interested in the case of invariant structure on Lie groups. We define semi-Sasakian Lie groups as a generalization of Sasakian Lie groups. Then we construct a semi-Sasakian structure on a group $G\ltimes \R^{n+1}$ for a projective Hessian Lie group $G$. Further, we describe examples of homogeneous Hessian Lie groups and corresponding semi-Sasakian Lie groups. The big class of projective Hessian Lie groups can be constructed by homogeneous regular domains in $\R^n$. The groups $\text{SO}(2)$ and $\text{SU}(2)$ belong to another kind of examples. Using them, we construct semi-Sasakian structures on the group of the Euclidean motions of the real plane and the group of isometries of the complex plane.

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.