o:1671 Karakteristični geometrijski objekti i projektivna preslikavanja Ajzenhartovih prostora i uopštenja Characteristic geometric objects and projective mappings of Eisenhart spaces and generalizations: doctoral dissertation : doctoral dissertation sr 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. Bibliografija: str. 102-113;Biobibliografija: str. [113-114]. Datum odbrane: 27.07.2020. Differential geometry 21866761 91552101 7836 91552100 21866761 2021-01-18T18:07:28.053Z 45 no 46 mentor Vladislava M., 1991- Milenković 2020 63 mentor Milan, 1984- Zlatanović 2020 63 predsednik komisije Ljubica Velimirović 2020 63 član komisije Zoran Rakić 2020 [6], 113 str. 1367290 http://phaidrabg.bg.ac.rs/o:1671 no yes 4 2021-01-18T18:07:28.320Z 70 prostori nesimetrične afine koneksije, generalisani Rimanovi prostori,generalisani Kelerovi prostori, geodezijska preslikavanja, skorogeodezijska preslikavanja, holomorfno projektivna preslikavanja,biholomorfno projektivna preslikavanja, Ajnštajnovi tenzori, tenzorNijenhuisa, invarijantni geometrijski objekti non-symmetric affine connection spaces, generalized Riemannian spaces, generalizedKählerian spaces, geodesic mappings, almost geodesic mappings, holomorphicallyprojective mappings, biholomorphically projective mappings, Einstein type tensors,Nijenhuis tensor, invariant geometric objects 514.763.2+514.763.4/.5+514.764.2/.4+514.774 P 150 1738 18A07 18A0701 2020