# 401-3532-08L Differential Geometry II

Semester | Spring Semester 2019 |

Lecturers | W. Merry |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | This is a continuation course of Differential Geometry I. Topics covered include: - Connections and curvature, - Riemannian geometry, - Gauge theory and Chern-Weil theory. |

Objective | |

Lecture notes | I will produce full lecture notes, available from my website at Link |

Literature | There are many excellent textbooks on differential geometry. A friendly and readable book that contains everything covered in Differential Geometry I is: John M. Lee "Introduction to Smooth Manifolds" 2nd ed. (2012) Springer-Verlag. For Differential Geometry II, the textbooks: - S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volume I (1963) Wiley, - I. Chavel, "Riemannian Geometry: A Modern Introduction" 2nd ed. (2006), CUP, are both excellent. The monograph - A. L. Besse "Einstein Manifolds", (1987), Springer, gives a comprehensive overview of the entire field, although it is extremely advanced. (By the end of the course you should be able to read this book.) |

Prerequisites / Notice | Familiarity with all the material from Differential Geometry I will be assumed (smooth manifolds, Lie groups, vector bundles, differential forms, integration on manifolds, principal bundles and so on). lecture notes for Differential Geometry I can be found on my webpage. |