Basic Riemannian Geometry
Bennet Chow Peng
Lu Lei Ni
-
Introduction
- Basic conventions(常規) and
formulas in Riemannian geometry
- Laplacian and Hessian
comparison theorems
- Geodesic polar coordinates
- First and second variations
of arc length and energy formulas
- Geometric application of
second variation
- Green
function
- Comparison theory for the
heat kernel
- Parametrix for the heat
equation
- Eigenvalues and
eigenfunctions of the Laplacian
- The determinant of the
Laplacian
- Monotonicity for harmonic
functions and maps
- Lie groups and left invariant
metrics
- Bieberbach Theorem
- Compendium of inequalities
- Notes and commentary