Title
Karakteristični geometrijski objekti i projektivna preslikavanja Ajzenhartovih prostora i uopštenja
Creator
Milenković, Vladislava M., 1991-
Copyright date
2020
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
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Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 27.07.2020.
Other responsibilities
mentor
Zlatanović, Milan, 1984-
predsednik komisije
Velimirović, Ljubica
član komisije
Rakić, Zoran
Academic Expertise
Prirodno-matematičke nauke
Academic Title
-
University
Univerzitet u Nišu
Faculty
Prirodno-matematički fakultet
Group
Odsek za matematiku i informatiku
Alternative title
Characteristic geometric objects and projective mappings of Eisenhart spaces and generalizations
: doctoral dissertation
Publisher
[V. M. Milenković]
Format
[6], 113 str.
description
Bibliografija: str. 102-113;
Biobibliografija: str. [113-114].
description
Differential geometry
Abstract (en)
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.
Authors Key words
prostori nesimetrične afine koneksije, generalisani Rimanovi prostori,
generalisani Kelerovi prostori, geodezijska preslikavanja, skoro
geodezijska preslikavanja, holomorfno projektivna preslikavanja,
biholomorfno projektivna preslikavanja, Ajnštajnovi tenzori, tenzor
Nijenhuisa, invarijantni geometrijski objekti
Authors Key words
non-symmetric affine connection spaces, generalized Riemannian spaces, generalized
Kählerian spaces, geodesic mappings, almost geodesic mappings, holomorphically
projective mappings, biholomorphically projective mappings, Einstein type tensors,
Nijenhuis tensor, invariant geometric objects
Classification
514.763.2+514.763.4/.5+514.764.2/.4+514.774
Subject
P 150
Type
Tekst
Abstract (en)
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.
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