Naslov (srp)

Karakteristični geometrijski objekti i projektivna preslikavanja Ajzenhartovih prostora i uopštenja

Autor

Milenković, Vladislava M., 1991-

Doprinosi

Zlatanović, Milan, 1984-
Velimirović, Ljubica
Rakić, Zoran

Opis (srp)

Bibliografija: str. 102-113;Biobibliografija: str. [113-114]. Datum odbrane: 27.07.2020. Differential geometry

Opis (eng)

The thesis deals with generalized Einstein spaces, Eisenhart-Riemannian spaces, Eisenhart-Kählerian spaces, Eisenhart-Kählerian spaces of the third type and spaces with non-symetric affine connection. Einstein type tensors are represented in the generalized Einstein spaces. Some relations of Einstein type tensors are obtained. Also, geodesic mappings of T-connected generalized Einstein spaces onto Riemannian space are considered. Geodesic mappins between Eisenhart-Riemannian space and Eisenhart-Kählerian space of the third type were studied, and specially the case when these spaces have the same torsion at corresponding points. Also, holomorphically projective mappings of two Eisenhart-Kählerian spaces were considered, and specially the case of equitorsion holomorphically projective mappings. We obtain quantites that are generalizations of the holomorphically projective tensor i.e. they are invariants. Almost geodesic mappings of the second type of spaces with non-symmetric affine connection are considered. A new form of the basic equation of almost geodesic mappings was found using the Nijenhuis tensor. Nijenhuis tensors of the first and second kind were introduced. Some relations of Nijenhuis tensors are obtained. Biholomorphically projective mappings and equitorsion biholomorphically projective mappings of two Eisenhart-Riemannian spaces were considered. Some relations and some ivariant geometric objects are obtained.

Jezik

srpski

Datum

2020

Licenca

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