Description:

Smooth manifold, tangent space differential forms, tensors, Riemannian metrics and manifold, covariant derivative, parallel transport, orientation of manifold, itegration on manifold and Stokes theorem.

Contents:

1. Smooth manifolds 2. Tangent and cotangent space 3. Tensors, differential forms 4. Orientation of manifold, integration on manifold 5. Stokes theorem 6. Riemannian manifold.

Recommended literature:

key references:
[1] J.M. Lee: Introduction to Smooth Manifolds, Springer, 2003.
recommended references:
[2] J. M Lee: Riemannian Manifolds: An Introduction to Curvature, Springer, 1997.
[3] M. Spivak: Calculus on Manifolds, Addison-Wesley Publishing Company, 1965.
[4] F. Morgan: Riemannian Geometry: A Begginer's Guide, Jones and Bartlett Publishers, 1993.

Keywords:

Differential geometry, Riemannian manifold, Stokes theorem.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar