Mathematics BSc
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
Strong Weak Prerequisites
Practice class
Strong:
Strong:
Geometry3L-p (mm1c1ge4m)
Lecture
Strong:
Strong:
Geometry3L-p (mm1c1ge4m)
Remarks
  • The practice class is not a prerequisite of the lecture.
Syllabus designed by:
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.