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Milenković, Vladislava M., 1991
Karakteristični geometrijski objekti i projektivna preslikavanja Ajzenhartovih prostora i uopštenja
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Academic metadata
Doktorska disertacija
Prirodnomatematičke nauke

Univerzitet u Nišu
Prirodnomatematički fakultet
Odsek za matematiku i informatiku
Other Theses Metadata
Characteristic geometric objects and projective mappings of Eisenhart spaces and generalizations
: doctoral dissertation
[V. M. Milenković]
[6], 113 str.
Bibliografija: str. 102113;
Biobibliografija: str. [113114].
Datum odbrane: 27.07.2020.
Differential geometry
Zlatanović, Milan, 1984 (mentor)
Velimirović, Ljubica (predsednik komisije)
Rakić, Zoran (član komisije)
The thesis deals with generalized Einstein spaces, EisenhartRiemannian spaces,
EisenhartKählerian spaces, EisenhartKählerian spaces of the third type and spaces
with nonsymetric affine connection. Einstein type tensors are represented in the
generalized Einstein spaces. Some relations of Einstein type tensors are obtained.
Also, geodesic mappings of Tconnected generalized Einstein spaces onto
Riemannian space are considered. Geodesic mappins between EisenhartRiemannian
space and EisenhartKählerian 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 EisenhartKählerian 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 nonsymmetric 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 EisenhartRiemannian
spaces were considered. Some relations and some ivariant geometric objects are
obtained.
nonsymmetric 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
514.763.2+514.763.4/.5+514.764.2/.4+514.774
P 150
Serbian
21866761
Tekst
The thesis deals with generalized Einstein spaces, EisenhartRiemannian spaces,
EisenhartKählerian spaces, EisenhartKählerian spaces of the third type and spaces
with nonsymetric affine connection. Einstein type tensors are represented in the
generalized Einstein spaces. Some relations of Einstein type tensors are obtained.
Also, geodesic mappings of Tconnected generalized Einstein spaces onto
Riemannian space are considered. Geodesic mappins between EisenhartRiemannian
space and EisenhartKählerian 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 EisenhartKählerian 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 nonsymmetric 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 EisenhartRiemannian
spaces were considered. Some relations and some ivariant geometric objects are
obtained.