Universitat Politècnica de Catalunya — Facultat de Matemàtiques i Estadística — Llicenciatura de Matemàtiques Geometria Diferencial 2 2007, primavera responsable: Xavier Gràcia http://www-ma4.upc.edu/˜ xgracia/gd2/

Temari Orientacions sobre la distribució de temes de geometria diferencial dins alguns textos bàsics.

Boothby  Conlon  Hicks  Lafontaine  Lee  Spivak  Warner

Varietats Aplicacions

{52–69 \atop 193–195} 67–70 1–5 {49–59 \atop 87–90} {11–24 \atop 30–37} 35–44 5–8

Vectors tangents Aplicació tangent 107–116 71–72 5–8

{64–65 \atop 92–95}

60–77

11–19

Subvarietats Estudi local d’aplicacions 69–81

{38–47 \atop 84–93}

13–15 66–69 155–170 55–66

22–33

Fibrat tangent Camps vectorials

{116–120 \atop 151–153} {74–76 \atop 109–110} 8–10 95–103 81–92 86–112 19–20 34–36 41

Fibrat cotangent 1-formes diferencials 177–183

{156 \atop 159–166}

56 181 124–138

{148–150 \atop 273}

{11–20 \atop 41}

Equacions diferencials 123–142 101–105

{10–12 \atop 93}

103–109 434–447 186–207

34–40

Camps tensorials Formes diferencials 199–223 189–212

{49–56 \atop 89–92}

163–184

{260–271 \atop 294–314}

{158–174 \atop 273–286}

54–69

Derivada de Lie 154–158

{107–110 \atop 167}

92–94 464–477 207–212

69–72

Grups de Lie  81–89 120–121 142–151  127–145  capítol IV  {314–318 \atop 481–491}  501–550  82–119

Subfibrats tangents {158–165 \atop 223–226} {110–120 \atop 277–280} 123–128 494–510 {244–264 \atop 293–296} {41–49 \atop 73–77}

Integració  {236–244 \atop 259–266}  {87–91 \atop 228–249}  98–105  capítol VI  349–363  325–356  138–153
Connexions  317–327  294–302  56–69

Varietats riemannianes

{183–191 \atop 317–350}

302–326 69–74 273–285

408–464

Varietats simplèctiques

{314–318 \atop 481–491}

Bibliografia

1. J. M. Lee, Introduction to smooth manifolds, Springer, New York, 2003.

2. W. M. Boothby, An introduction to differentiable manifolds and riemannian geometry, Academic Press, San Diego, 1986

3. L. Conlon, Differentiable manifolds: a first course, Birhäuser, Boston, 1993.

4. N. J. Hicks, Notes on differential geometry, Van Nostrand, London, 1971.

5. J. Lafontaine, Introduction aux variétés différentielles, Presses Universitaires de Grenoble, Grenoble, 1996.

6. M. Spivak, A comprehensive introduction to differential geometry vol. I (3rd ed.), Publish or Perish, Houston, 1999.

7. F. W. Warner, Foundations of differentiable manifolds and Lie groups, Springer, New York, 1983.

8. R. Abraham, J. E. Marsden and T. Ratiu, Manifolds, tensor analysis, and applications (2nd ed.), Springer, New York, 1988.

9. D. Barden and C. Thomas, An introduction to differential manifolds, Imperial College Press, 2003

10. M. Berger and B. Gostiaux, Differential geometry: manifolds, curves, and surfaces, Springer, New York, 1988.

11. R. Bott and L. W. Tu, Differential forms in algebraic topology, Springer, New York, 1982.

12. C. Currás Bosch, Geometria diferencial: varietats diferenciables i varietats de Riemann, Edicions Universitat de Barcelona, Barcelona, 2003.

13. W. D. Curtis and F. R. Miller, Differential manifolds and theoretical physics, Academic Press, Orlando, 1985.

14. J. Dieudonné, Éléments d’analyse vols. 3 i 4, Gauthier-Villars, Paris, 1970 i 1971.

15. J. Girbau, Geometria diferencial i relativitat, Publicacions de la UAB, Bellaterra, 1993.

16. C. Godbillon, Géometrie différentielle et mécanique analytique, Hermann, Paris, 1969.

17. S. Kobayashi and K. Nomizu, Foundations of differential geometry vol. I, John Wiley, New York, 1963.

18. R. H. Wasserman, Tensors and manifolds with applications to physics (2nd ed.), Oxford University Press, Oxford, 2004.

5-2-2007