Differential Geometry Notes Spring? 1989

by Bob Jantzen

Tensor algebra, curvilinear coordinates, manifolds, Riemannian and pseudo-Riemannian geometry, some Lie group theory.

These are very rough notes written for one student in an independent study. See the more polished but not quite equivalent notes from 1991.

• dgn1989-1.pdf Tensors on R^n
• dgn1989-2.pdf Determinants, antisymmetrization, wedge products
• dgn1989-3.pdf Volume and determinants
• dgn1989-4.pdf Duality
• dgn1989-5.pdf Reinterpreting elementary linear algebra
• dgn1989-6.pdf Wedge product and volume revisited, inner products on V extended to tensor algebra,
  missing section on the tangent space in multivariable calculus?
• dgn1989-7.pdf Coordinate transformations, computing metric and connection components
• dgn1989-8.pdf Example of computing metric and connection components: spherical coordinates