"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Noneuclidean geometry
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MG022
5
2+1+0
6
optional
Matematică
Teaching Staff in Charge
Assoc.Prof. VARGA Csaba Gyorgy, Ph.D., csvarga@cs.ubbcluj.ro
Aims
The main purpose of the course consists in construction of the principal instruments which are necessary in studying the the Non-Euclidian geometry. The following notions and results are studied: Riemannian metric, Levi-Civita conexion,
geodesics, Riemannian curvature tensor, sectional curvature, space of constant curvature, elliptic geometry, hyperbolic geometry, euclidian models.
Content
1. Fiber bundles
2. Riemannian metric
3. Levi-Civita conexion
4. Geodesics
5. Riemannian curvature tensor
6. Sectional curvature
7. Space of constant curvature
8. Elliptic geometry
9. Hyperbolic geometry
10.Euclidian models.
References
1. M.P. do Carmo, Riemannian geometry, Birkhauser, 1992
2. S. Gallot, D. Hulin, J. Lafontain, Riemannian geometry, Springer-Verlag, Berlin, 1990
3. H.S.M. Coxeter, Non-Euclidian Geometry, Math. Assoc. of America , 1998
4. B.V. Cutuzov, Geometria lui Lobacevschi si elementele de baza ale geometriei, Editura Tehnica, 1952
5. I.M. Jaglom, Galilei relativitasi elv, Gondolat, Budapest, 1985
Assessment
Exam