Course Title: 
Riemannian Geometry 

Spring 2012 
Text: 
Isaac Chavel, Riemannian Geometry  A Modern Introduction, 2nd edition, Cambridge 2006 
Additional Texts in Riemannian Geometry.
 Thierry Aubin, A Course in Differential Geometry, Graduate Studies in Mathematics 27, Providence, American Mathematical Society, 2000.
 Richard L. Bishop & Richard J. Crittenden, Geometry of Manifolds, Pure and Applied Mathematics 15, New York, Academic Press, 1964.
 Richard L. Bishop & Samuel I. Goldberg, Tensor Analysis on Manifolds, orig. New York, Macmillan Company, 1968; repr. New York, Dover, 1980.
 Simon Brendle, Ricci Flow and the Sphere Theorem, Graduate Studies in Mathematics 111, Providence, American Mathematical Society, 2010.
 Jeff Cheeger & David G. Ebin, Comparison Theorems in Riemannian Geometry, Amsterdam, North Holland Publ. Co., 1975.
 Manfredo P. do Carmo, Riemannian Geometry, Mathematics: Theory & Applications, Birkhaüser, Boston, 1992.
 Luther P. Eisenhart, Riemannian Geometry, Princeton Landmarks in Mathematics, Princeton, Princeton University Press, (orig. 1950) 1997.
 Sylvestre Gallot, Dominique Hulin & Jaques Lafontaine, Riemannian Geometry, Universitext, New York, Springer, 1990.
 Noel J. Hicks, Notes on Differential Geometry, Van Nostrand Reinhold Mathematicsl Studies 3, New York, Van Nostrand Reinhold Co., 1963.
 Jürgen Jost, Riemannian Geometry and Geometric Analysis, Universitext, New York, Springer, 1995.
 Hermann Karcher, Riemannian Comparison Constructions, in book: S. S. Chern, Global Differential Geometry, MAA Studies in Mathematics 27, Providence, Mathematical Association of America (1989) 170222.
 Wilhelm Klingenberg, Riemannian Geometry, de Gruyter Studies in Mathematics 1, Berlin, Walter de Gruyter & Co., 1982.
 Shoshichi Kobayashi & Katsumi Nomizu, Foundations of Differential Geometry, Tracts in Mathematics 15, New York, Interscience Publ., 1963.
 John M. Lee, Riemannian Manifolds: An Introduction to Curvature, Graduate Texts in Mathematics 176, New York, Springer, 1997.
 Peter Petersen, Riemannian Geometry, Graduate Texts in Mathematics 171, New York, Springer, 1998.
 Takashi Sakai, Riemannian Geometry, Translates of Mathematical Monographs 149, Providence, American Mathematical Society, 1992.
 Richard Schoen & ShingTung Yau, Lectures in Differential Geometry, Conference Proceedings and Lecture Notes in Geometry and Topology 1, Cambridge, International Press, 1994.
do Carmo's is perhaps the most readable. Lee's text, based on a course at UW, is very thorough. Sakai's was my first choice but it is expensive. Gallot, Hulin & Lafontaine is loved by topologists but pulls its punches. Karcher's is a beautiful presentation of comparison theory.
Schoen and Yau's is a delicious union of research papers. Hicks develops classical, vector and moving frame notation sidebyside.
Last updated: 1 / 23 / 12