Riemannian Geometry II

The Bochner technique. Geometry of the Laplace operator and its eigenvalues. Holonomy and symmetric spaces. Positive and non-negative curvature. Sequences of Riemannian manifolds. The Yamabe problem. Einstein manifolds. Sphere Theorems. Other topics.

References:
BESSE, A. – Einstein manifolds, 1987.
CHAVEL, I. – Riemannian Geometry: A Modern Introduction, Cambridge U. Press, 1993.
CHEEGER, J., EBIN, D. – Comparison Theorems on Riemannian Geometry, North-Holland, 1975.
JOST, J. – Riemannian Geometry and Geometric Analysis, Berlin Heidelberg, New York, Springer-Verlag, 1995.
PETERSEN, P. Riemannian Geometry, Graduate Texts in Mathematics, Springer-Verlag, 2006.
SCHOEN, R., YAU S.-T., – Lectures on Differential Geometry, International Press, 1994.