# Differential Geometry I (미분기하학)

## Class Info

Class Number: Math 372002
Dates: Sep 3 2012 - Dec 8 2012
Room: NS 318
Meeting time:
 Monday 13:30 - 14:45 Friday 13:30 - 14:45

Purpose: Introduction to Differential Geometry; Curves in Space
Text: Barrett O'Neill, Elementary Differential Geometry, Rev. 2nd Ed., Elsevier 2006
 Links Homework Material covered Leonard Susskind on General Relativity: Lecture 1 of 15

The purpose of this course is to introduce basic concepts of Differential Geometry and use them to study the properties of curves in space.

## Syllabus

 Week Chapters Topics 1 1.1 Euclidean Space. Differentiability. 2 1.2-3 Tangent Vectors. Directional Derivatives. 3 1.4 Curves in R^3. 4 1.5-6 1-Forms. Differential Forms. 5 1.7 Mappings. 6 2.1 Dot Product. 7 2.2-3 Midterm Exam. Curves. The Frenet Formulas. 8 2.4 Arbitrary-Speed Curves. 9 2.5-6 Covariant Derivatives. Frame Fields. 10 2.7-8 Connection Forms. The Structural Equations. 11 3.1 Isometries of R^3. 12 3.2 The Tangent Map of an Isometry. 13 3.3 Orientation 14 3.4 Euclidean Geometry 15 3.5 Congruence of Curves. Final Exam.