Tópicos para apresentações de seminários:

• Curvatura e crescimento do grupo fundamental
• O grupo de holonomia de variedades Riemannianas
• Conexões em fibrados principais
• O teorema de Toponogov
• O teorema de Bishop-Gromov
• O teorema da esfera de Rauch-Berger-Klingenberg
• O teorema de decomposição de Cheeger-Gromoll
• Teoria de Hodge
• Submersões Riemannianas
• O Laplaciano em variedades Riemannianas
• A técnica de Bochner
• Espaços simétricos Riemannianos
• Variedades Kählerianas
• Convexidade em variedades Riemannianas
• O método do referencial móvel
• O princípio do máximo em variedades Riemannianas
• Variedades de curvatura não-positiva

• Versão em pdf que sofrerá modificações no decorrer do curso.
• Versão de 27/06, a ser expandida: pdf
• Versão de 05/07, a ser expandida: pdf

• Livros básicos
  • MR0651516 (84b:53001) do Carmo, Manfredo Perdigão. Geometria riemanniana. (Portuguese) [Riemannian geometry] Projeto Euclides [Euclid Project], 10. Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1979. ix+238 pp.
  • MR1083149 (91j:53001) Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques. Riemannian geometry. Second edition. Universitext. Springer-Verlag, Berlin, 1990. xiv+284 pp. ISBN: 3-540-52401-0
  • MR1271141 (95j:53001) Chavel, Isaac. Riemannian geometry---a modern introduction. Cambridge Tracts in Mathematics, 108. Cambridge University Press, Cambridge, 1993. xii+386 pp. ISBN: 0-521-43201-4; 0-521-48578-9
  • MR1330918 (95m:53003) Klingenberg, Wilhelm P. A. Riemannian geometry. Second edition. de Gruyter Studies in Mathematics, 1. Walter de Gruyter & Co., Berlin, 1995. x+409 pp. ISBN: 3-11-014593-6
  • MR1480173 (98m:53001) Petersen, Peter. Riemannian geometry. Graduate Texts in Mathematics, 171. Springer-Verlag, New York, 1998. xvi+432 pp. ISBN: 0-387-98212-4
  • MR1390760 (97f:53001) Sakai, Takashi. Riemannian geometry. Translated from the 1992 Japanese original by the author. Translations of Mathematical Monographs, 149. American Mathematical Society, Providence, RI, 1996. xiv+358 pp. ISBN: 0-8218-0284-4
  • MR1261641 (95e:53002) Willmore, T. J. Riemannian geometry. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993. xii+318 pp. ISBN: 0-19-853253-9
  • MR2394158 (2009c:53043) Cheeger, Jeff; Ebin, David G. Comparison theorems in Riemannian geometry. Revised reprint of the 1975 original. AMS Chelsea Publishing, Providence, RI, 2008. x+168 pp. ISBN: 978-0-8218-4417-5
  
  
• Fundamentos da teoria
  • MR0152974 (27 #2945) Kobayashi, Shoshichi; Nomizu, Katsumi. Foundations of differential geometry. Vol I. Interscience Publishers, a division of John Wiley & Sons, New York-Lond on 1963 xi+329 pp.
  • MR0238225 (38 #6501) Kobayashi, Shoshichi; Nomizu, Katsumi. Foundations of differential geometry. Vol. II. Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney 1969 xv+470 pp.
  
  
• Tópicos avançados
• MR1990032 Berndt, Jürgen; Console, Sergio; Olmos, Carlos. Submanifolds and holonomy. Chapman & Hall/CRC Research Notes in Mathematics, 434. Chapman & Hall/CRC, Boca Raton, FL, 2003. x+336 pp. ISBN: 1-58488-371-5
• MR0867684 (88f:53087) Besse, Arthur L. Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 10. Springer-Verlag, Berlin, 1987. xii+510 pp. ISBN: 3-540-15279-2
• MR0514561 (80k:53081) Helgason, Sigurdur. Differential geometry, Lie groups, and symmetric spaces. Pure and Applied Mathematics, 80. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. xv+628 pp. ISBN: 0-12-338460-5
• MR0928600 (88k:53002) Wolf, Joseph A. Spaces of constant curvature. Fifth edition. Publish or Perish, Inc., Houston, TX, 1984. xviii+412 pp. ISBN: 0-914098-07-1
• MR1004008 (90g:53058) Salamon, Simon. Riemannian geometry and holonomy groups. Pitman Research Notes in Mathematics Series, 201. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. viii+201 pp. ISBN: 0-582-01767-X