Connections with torsion on riemannian manifolds and generalizations

[M. D. Maksimović]

[4], 123 lista

Biografija: list 121 Bibliografija: listovi 122-123

Differential geometry

The thesis deals with connections with torsion on different manifolds. Semi-symmetric connections, quarter-symmetric connections and Eisenhart connection are studied. Some semi-symmetric metric connections are investigated on pseudo- Riemannian manifolds and then applied to Lorentzian manifolds and to the theory of relativity. A quarter-symmetric metric connection is studied on generalized Riemannian manifolds, and some relations for the holomorphically projective curvature tensor and the Weyl projective curvature tensor are established in Kähler and co-Kähler manifolds. A new quartersymmetric non-metric connection is also introduced. Results for ET-conformal and ET-concircular mappings of generalized Riemannian manifolds with Eisenhart connection are expanded. ET-conharmonic mappings are introduced and their invariant geometric objects are found.

Tenzor torzije, polu-simetrična koneksija, četvrt-simetrična koneksija, pseudo-Rimanove mnogostrukosti, generalisane Rimanove mnogostrukosti, Kelerove mnogostrukosti, ko- Kelerove mnogostrukosti, Ajnštajnove mnogostrukosti, kvazi- Ajnštajnove mnogostrukosti, Lorencove mnogostrukosti, idealan fluid, konformna preslikavanja, koncirkularna preslikavanja, konharmonijska preslikavanja, projektivna preslikavanja, invarijantni geometrijski objekti, tenzori krivine

Torsion tensor, semi-symmetric connection, quarter-symmetric connection, pseudo-Riemannian manifolds, generalized Riemannian manifolds, Kähler manifolds, co-Kähler manifolds, Einstein manifolds, quasi-Einstein manifolds, Lorentzian manifolds, perfect fluid space-time, conformal mappings, concircular mappings, conharmonic mappings, projective mappings, invariant geometric objects, curvature tensors

514.763.4/.5+514.764.2/.4(043.3)

P150

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