Seminar za geometriju, obrazovanje i vizualizaciju sa primenama, 31. maj 2012.

• 28. Maj,  2012
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 Naredni sastanak Seminara za geometriju, obrazovanje i vizualizaciju sa primenama održaće se u četvrtak, 31. maja 2012. u 17h, sala 301f, MI SANU.

U okviru Seminara ovog puta će biti održana dva predavanja.

Prvi predavač: Svetislav Minčić, Prirodno-matematički fakultet, Niš

Naslov prvog predavanja: On curvature tensors obtained by two non-symmetric affine connections

Sadržaj: In the works [1,2,3,4,5,6,7,8] curvature tensors are considered by polylinear mappings, using non-symmetric connections, and in the rest works from the References the curvature tensors are obtained by help of Ricci-type identities in local coordinates. In the present paper this problem is considered more generally by help of polylinear mappings and eight curvature tensor fields are obtained. Further, it is proved that among these fields five of them are independent, while the rest are linear combinations of the cited five fields.

[1] Das, L.S., Nivas, R., Ali, S., Ahmad,  M., Study of submanifolds immersed in a manifolds with quater symmetric semi symmetric connection, Tensor, N.S, Vol 65, (2004), 250--260.
[2] Imai, T., Notes on semi-symmetric metric connections, Tensor, N.S, Vol 24, (1972), 293-296.
[3] Mincic, S. M., On curvature tensors of non-symmetric affine connection, Acta et Commentations Universitatis Tartuensis de Mathematica, Vol. 9, (2005), 13--20.
[4] Mincic, S. M., Some characteristics of curvature tensors of nonsymmetric affine connexion, Novi Sad J. Math., 29, No.3, (1999), 169--186.
[5] Mincic, S. M., Velimirovic, Lj. S., Differential geometry of manifolds (in Serbian), Faculty of Science and Mathematics, University of Nis, 2011.
[6] Prvanovic, M., Four curvature tensors of non-symmetric affine connexion (in Russian), Proceedings of the conference "150 years of Lobachevski geometry", Kazan 1976, Moscow 1997, 199--205.
[7] Yano, K., On semi-symmetric metric connection, Revne Roum. de Math. pures et appl., 15, (1970), 1579--1581.


Naslov drugog predavanja: On Ricci type identities in manifolds with non-symmetric affine connection

Sadržaj: In the paper [1] using polylinear mappings, we have obtained several curvature tensors in the space $L_N$ with non-symmetric affine connection $\nabla$. Five of these tensors are independent, and the others are linear combinations of the mentioned ones. In the present work, by polylinear mappings, Ricci type identities are examined.


[1] S. Minčić, On curvature tensors obtained by two non-symmetric affine connections, submitted.



Drugi predavač: Milan Zlatanović, Prirodno-matematički fakultet, Niš

Naslov predavanja: Generalisani Finslerovi prostori

Sadržaj: Prateći ideju A. C. Shamihoke [1,2,3,4] definišemo generalisani Finslerov prostor, kao $N$dimenzionalnu mnogostrukost sa nesimetričnim osnovnim tenzorom $g_{ij}(x,\dot{x})$ koji zadovoljava odgovarajuće jednačine. Na osnovu nesimetrije koneksije definišemo četiri vrste kovarijantnog diferenciranja u Rundovom smislu i dobijamo identitete Ricijevog tipa. U pomenutim identitetima pojavljuje se četiri tenzora krivine i veličine koje "liče" na tenzore a nisu tenzori, nazvane su "pseudotenzori". Dalje, ispitujemo svojstva simetrije tenzora krivine po paru indekasa, cikličnu simetriju i antisimetriju. Delimično je rešena i geometrijska interpretacija tenzora krivine u generalisanom Finslerovom prostoru.

[1] A. C. Shamihoke, A Note on a Curvature Tensor in a Generalized Finsler space,Tensor, N.S., 15 (1964), 20-22.
[2] A. C. Shamihoke, Hypersurfaces of a Generalised Finsler Space, Tensor, N.S., 13 (1963), 129-144.
[3] A. C. Shamihoke, Parallelism and Covariant Differentiation in a Generalized Finsler Space of $n$dimensions, Riv. Mat. Univ. Parma, II. Ser. 5, (1964),189-200.
[4] A. C. Shamihoke, Some Properties of a Curvature Tensors in a Generalised Finsler Space, Tensor, N.S., 12 (1962), 97-109.

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