Faculty of Mathematics and Computer Science

Differential manifolds |

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 Lect. BLAGA Paul Aurel, Ph.D., pablaga@cs.ubbcluj.ro |

Aims |

The course follows in a natural way "Curves and Surfaces" from second semester in the first year by studying the main geometrical objects associated to a differentiable manifolds. The seminars supply by examples,applications, execices and problems the theoretical material given at the course. |

Content |

1.The space R^n from algebraic and topological point of view. Differentiable mappings.
The locally diffeomorphism theorem and consequences. The rank theorem. Regular points and critical points. 2. Differentiable manifolds. Examples. Topological properties. Differentiable mappings between manifolds. The tangent space and the tangent map. The cotangent space and the cotangent map. Differentiable submanifolds. Immersions, submersions, embedings. 3. Fiber bundles. Vector bundles. Constructions with vector bundles. 4. Vector fields on a manifold. Globally and locally flows. Integrability and completeness. Lie algebra of vector fields. |

References |

1. Bredon, G.E., Topology and Geometry, Springer-Verlag, 1993.
2. Enghis, P., Tarina, M., Curs de geometrie diferentiala (lito) Univ. Cluj-Napoca, 1987. 3. Ianus, S., Geometrie diferentiala cu aplicatii in teoria relativitatii, Ed. Academiei, 1983. |

Assessment |

Exam. |