Universitatea "Babeş-Bolyai" din Cluj-Napoca

Facultatea de Matematică şi Informatică
FISA DISCIPLINEI

Geometrii neeuclidiene

Noneuclidean geometry

Cod	Semes- trul	Ore: C+S+L	Credite	Tipul	Sectia
MG022	5	2+1+0	6	optionala	Matematică (Mathematics)

Cadre didactice indrumatoare

Teaching Staff in Charge

Conf. Dr. VARGA Csaba Gyorgy, csvarga@cs.ubbcluj.ro

Obiective

Aims

Cursul are ca scop constructia principalelor instrumente necesare in studiul geometriilor neeuclidiene din punct de vedere diferential si din punct de vedere sintetic. Cursul este orientat in urmatoarele directii: fibratul tangent, metrica Riemann, conexiunea Levi-Civita, geodezice, tensorul de curbura a lui Riemann, curbura sectionala, spatii cu curbura constanta, geometria eliptica, geometria hiperbolica, modele euclidiene.

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.

Continut

1. Fibratul tangent 2. Metrica Riemann 3. Conexiunea Levi-Civita 4. Geodezice 5. Tensorul e curbura a lui Riemann 6. Curbura sectionala 7. Spatii cu curbura constanta 8. Geometria eliptica 9. Geometria hiperbolica 10. Modele euclidiene

Bibliografie

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

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