Geometrii neeuclidiene | Noneuclidean geometry |
trul |
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(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. |
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 |
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 |
Evaluare | Assessment |
Examen |
Exam |