Differential Geometry

Subject 620-640 (2009)

Note: This is an archived Handbook entry from 2009. Search for this in the current handbook

Credit Points: 12.50
Level: 9 (Graduate/Postgraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2009:

Semester 2, - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable


Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 36 hours comprising 2 one-hour lectures per week and 1 one-hour practice class per week.
Total Time Commitment: 3 contact hours plus 7 hours private study per week.
Prerequisites: None.
Corequisites: None.
Recommended Background Knowledge: It is recommended that students have completed subjects in vector analysis (equivalent to 620-231 [2008] Vector Analysis) and metric spaces (equivalent to 620-311 [2008] Metric Spaces).
Non Allowed Subjects: None.
Core Participation Requirements: It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their participation are encouraged to discuss this with the subject coordinator and the Disability Liaison Unit.


Prof Joachim Hyam Rubinstein
Subject Overview: In this course students will become familiar with the basic notions of Riemannian metrics and curvature, geodesics and concrete examples such as hypersurfaces in Euclidean space, Lie groups and homogeneous spaces. Some fundamental tools of global differential geometry will be covered, for example, the Cartan-Hadamard theorem for manifolds of non positive curvature and O'Neill's formula for the curvature of homogeneous spaces.

Objectives: After completing this subject, students will gain:
- An understanding of the basic notions of smooth manifolds and Riemannian metrics, including connections and vector bundles;
- the ability to do calculations in local coordinates;
- a knowledge of the important examples of Lie groups and symmetric spaces;
- the ability to compute curvatures for homogeneous spaces;
- the ability to pursue further studies in this and related areas.
Assessment: Up to 60 pages of written assignments (60%: three assignments worth 20% each, due early, mid and late in semester), a two-hour written examination (40%, in the examination period).
Prescribed Texts: TBA
Recommended Texts: TBA
Breadth Options:

This subject is not available as a breadth subject.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills: Upon completion of this subject, students should gain the following generic skills:
- Problem-solving skills including the ability to engage with unfamiliar problems and identify relevant solution strategies
- Analytical skills through the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis
- Time management skills: the ability to meet regular deadlines while balancing competing commitments
Related Majors/Minors/Specialisations: R05 RM Master of Science - Mathematics and Statistics

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