240A Winter 2018
# 240A Winter 2018

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**Differental Geometry ** Math 240A

MWF 11:00-11:50 PM,

BAINER 1060

Instructor: Prof. Joel Hass

Office: 2222 MSB (Mathematical Sciences Building)

Office hours: Monday 1:10-2 PM, Wednesday 10-11:50 AM.

(530) 601-4444 Extension 4003

email: hass(at)math.ucdavis.edu

(In addition, I plan to organize an optional exercise review session each week.
The time will depend on when the most people can come.)

**Course Contents**:
The Department syllabus can be found at
Math 240a - Syllabus.

** Textbook: **
The textbook for the course is * Riemannian Geometry* by M. do Carmo.
This book can be very dense, so you can expect to take a lot of time to read a page if you
want to fully understand it.
There are numerous other books on differential geometry that would be useful to look at.
Some worth considering are:

F. W. Warner, "Foundations of Differential Manifolds and Lie Groups";

W. Boothby, "An Introduction to Differentiable Manifolds and Riemannian Geometry";

P. Petersen, "Riemannian Geometry";

J. Jost, "Riemannian Geometry and Geometric Analysis";

I. Chavel, "Riemannian Geometry: A Modern Introduction".

Gallot, Hulin and Lafontaine, Riemannian Geometry

Lee, Riemannian Manifolds: An Introduction to Curvature

A Panoramic View of Riemannian Geometry, Marcel Berger, Springer 2003.

Spivak, A Comprehensive Introduction to Differential Geometry

** Notes: **
You can find many lecture notes on this subject online.
For example:

http://www.cis.upenn.edu/~cis610/Riemann.pdf

http://www.math.brown.edu/~kahn/RiemannianGeometryIntroII.pdf

http://www.math.uiuc.edu/~ekerman/riemannian_geometry_lecture_notes.pdf

http://www.maths.manchester.ac.uk/~khudian/Teaching/Geometry/GeomRim11/riemgeom11.pdf

http://www.maths.tcd.ie/~dwilkins/Courses/425/RiemGeom.pdf

http://www.sci.utah.edu/~fletcher/RiemannianGeometryNotes.pdf

http://math.stanford.edu/~schoen/math217a/ps13_2.pdf
**
GRADES:
**
There will be a take home exam during Finals week.
(40% of grade).

There will also be regular homework assignments (30%) and
a project involving presenting a topic (30%). This wll be discussed
in class.

** Homework **
Homework will be listed here when assigned.

HW 1, due Monday 1/21: Chapter 1, Exercises 1,2,3,6.

HW 2, Due Monday, 2/12/18, Chapter 2: Exercises 3,4.

HW 3, Due Monday 2/26/18, Chapter 3: Exercises 4, 7.

HW 4, Due Friday, 3/9/18 Chap 3: Exercises 8, 9.

HW 5, Due Friday, 3/16/18 Chap 4: Exercise 4.

Compute all Jacobi fields for the geodesic in Euclidean
3-space R3 given by g(t) = (t,0,0).