Course Information
Course title
微分幾何二
DIFFERENTIAL GEOMETRY (II) 
Semester
93-2 
Designated for
COLLEGE OF SCIENCE  GRADUATE INSTITUTE OF MATHEMATICS  
Instructor
蔡宜洵 
Curriculum Number
MATH7302 
Curriculum Identity Number
221 U2940 
Class
 
Credits
Full/Half
Yr.
Half 
Required/
Elective
Elective 
Time
Tuesday 6,7,8(13:20~16:20) 
Room
舊數103 
Remarks
研究所數學組基礎課 
 
Course introduction video
 
Table of Core Capabilities and Curriculum Planning
Table of Core Capabilities and Curriculum Planning
Course Syllabus
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Course Description

I.Contents:
a) Local differential geometry/tensor calculus:
metric,connection, curvature, geodesics, Jacobi fields, variational formulas, comparision theorems.
b) General theory on vector/fiber bundles:
classification, characteristic classes, homotopy exact sequences, examples.
c) de Rham theory and Hodge theory:
differential forms, de Rham theorem, analytical proof of Hodge theory in Riemannian case.
d) Complex differential geometry:
complex and Kahler manifolds, projective algebraic manifolds, holomorphic curvature, Hodge metrics, line bundles.
*) Selective advanced topics (if the time permits).
II.Course prerequisite:
III.Reference material ( textbook(s) ):
Textbooks:
B.A. Dubrovin, A.T. Fomenko, S.P. Novikov: `Modern Geometry-methods and applications`, vol 1, 2.
Reference books:
B.A. Dubrovin, A.T. Fomenko, S.P. Novikov: `Modern Geometry-methods and applications`, vol 3.
Griffiths/Harris: Principles of algebraic geometry.
IV.Grading scheme:
a) Homework (20-30 %)
b) Final exam (70-80 %) 

Course Objective
 
Course Requirement
 
Student Workload (expected study time outside of class per week)
 
Office Hours
 
Designated reading
 
References
 
Grading
   
Progress
Week
Date
Topic
No data