Faculty of Mathematics and Computer Science

Noneuclidean geometry |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

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 |