Mathematics BSc
Course description
2013.
Course description
2013.
Differential geometry of manifolds
Hours lect+pc |
Credits lect+pc |
Assessment | Specialization | Course code lect/pc |
Semester | Status |
---|---|---|---|---|---|---|
2 + 2 | 2 + 3 | exam + term grade |
pure math. | mm1c1dg6m mm1c2dg6m |
6 | recommended |
Course coordinator
Strong | Weak | Prerequisites | |
---|---|---|---|
Practice class | |||
Strong:
Introduction to differential geometryL-p
(mm1c1dg5m)
| |||
Strong:
Geometry3L-p
(mm1c1ge4m)
| |||
Lecture | |||
Strong:
Introduction to differential geometryL-p
(mm1c1dg5m)
| |||
Strong:
Geometry3L-p
(mm1c1ge4m)
|
Prerequisites
Multivariable calculus, linear algebra, topology.
Literature
- Frank W. Warner: Foundations of differentiable manifolds and Lie groups. Scott, Foresman and Company, Glenview, 1971.
- Manfredo P. do Carmo: Differential geometry of curves and surfaces. Prentice-Hall, New-Jersey, 1976.
- B. Csikós: Differential Geometry. Lecture notes.
Syllabus
- Differentiable manifolds. Smooth maps, diffeomorphisms. Tangent and tensor bundles of a manifold. Smooth tensor fields. Lie derivative. Submanifolds. Integrability of distributions.
- Differential forms on a manifold. Exterior product. Exterior differentiation. De Rham cohomology. Integration of differential forms. Stokes’s theorem. Volume measure of a Riemannian manifold.
- Affine connection on a manifold. Covariant derivatives. Parallel translation along a curve. Levi-Civita connection of a Riemannian manifold. Curvature tensor. Geodesics.