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Riemannian Geometry

(Spring 2019)


Notices

1. Final exam: 2019.06.25, 9:45-11:45 am, Room 5404


Lectures and excercises



Lecture 1 Introduction; Riemannian metric

Lecture 2 Existence of Riemannian metrics; Metric structure; Riemannian measure.

Lecture 3 Divergence Theorem; Energy functional and geodesics

Lecture 4 Geodesic equations; Exponetial map, normal coordinates, and polar coordinates

Lecture 5 Local minimizing property of geodesics

Lecture 6 Local isometry preserves geodesics; Hopf-Rinow Theorem; injectivity radius and cut locus

Lecture 7 Existence of shortest geodesic in given homotopy classes Lecture note

Lecture 8 Riemannian covering map; Affine connection and covariant derivatives of vector fields along a curve.

Lecture 2019/05/07-09 Morse Index Theorem.

Lecture 2019/06/06 Splitting Theorem.

作业 1 3月14日(周四)交:

作业 2 3月28日(周四)交:

作业 3 4月11日(周四)交:


References


Tutorials

助教: 严海涛 hawthorne_isis@163.com


Differential Geometry 2018 Fall


纯粹数学前沿 2018 夏季学期


Riemannian Geometry 2018 Spring


Differential Geometry 2017 Fall


Riemannian Geometry 2017 Spring


Teaching in Durham