MATH41320: Riemannian Geometry

• Differential Geometry.

• None

• Differential Geometry.

• Provide a knowledge of the intrinsic geometry of Riemannian manifolds. This is a significant generalisation of the metric geometry of surfaces in 3-space.

• The metric geometry of Riemannian manifolds.
• Geodesics.
• Various notions of curvature, and their effect on the geometry of a Riemannian manifold.
• Second variation formula, global comparison theorems with applications.

Subject-specific Knowledge:

• Have a knowledge and understanding of Riemannian geometry demonstrated through the following topic areas:
• Riemannian manifolds;
• geodesics;
• Levi-Civita connection;
• curvature;
• global comparison results.

Subject-specific Skills:

• Have developed advanced technical and scholastic skills in the area of the geometry of surfaces in 3-space.

Key Skills:

• Have developed an appreciation of high-level mathematical reasoning.
• Have developed the ability to present well-reasoned arguments and operate in complex and specialised contexts.

• Teaching is by lectures through which the main body of knowledge is made available.
• Students do regular formative work solving problems to gain insight into the details of the relevant theories and procedures.
• End of year examinations assess the learning.

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

If you have a question about Durham's modular degree programmes, please visit our Help page. If you have a question about modular programmes that is not covered by the Help page, or a query about the on-line Postgraduate Module Handbook, please contact us.

Prospective Students: If you have a query about a specific module or degree programme, please Ask Us.

Current Students: Please contact your department.