Riemann Geometry

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

-

Course Contents

Riemann metric, Riemann manifold, Riemann connection, geodesics, curvatures, tensors on Riemann manifolds, Riemann submanifolds, second fundamental form, shape operator of a Riemann submanifold, Gauss, Ricci and Codazzi equations.

Weekly Schedule

1) Differentiable manifold, tangent space
2) Immerses and embeddings, manifold examples, topology of manifolds
3) Riemann metric
4) Affine connections, Riemann connections
5) Geodesics
6) Convex neighborhoods
7) Curvatures
8) Midterm exam
9) Sectional curvature
10) Ricci curvature and scalar curvature
11) Tensors on Riemannian manifolds
12) Jacobi equation, second fundamental form
13) Complete manifolds, Hopf-Rinow and Hadamard Theorems
14) Spaces of constant curvature
15) Space forms
16) Final exam

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Lecture
3) Lecture
4) Lecture
5) Question-Answer
6) Question-Answer
7) Question-Answer
8) Question-Answer
9) Discussion
10) Discussion
11) Discussion
12) Drill and Practice
13) Drill and Practice
14) Drill and Practice
15) Drill and Practice
16) Brain Storming
17) Self Study
18) Self Study
19) Self Study
20) Self Study
21) Problem Solving
22) Problem Solving
23) Problem Solving

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	40%
Contribution of Final Examination to Course Grade	60%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required