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Pubblicato
Corchete y curvatura
Parole chiave:
Lie Bracket, Curvature tensor, Affine connection, 2000 Mathematics Subject Classification, Primary: 53B20, Secondary: 53B21 (es)##submission.downloads##
La primera parte del artículo presenta al corchete de Lie asociado al problema de la comutatividad de dos flujos. En la segunda parte se introducen
las definiciones básicas de conexión y curvatura en fibrados vectoriales, subrayando la relación corchete-curvatura. Finalmente, usando conexiones afines
localmente definidas, se da una demostración original y sencilla de un teorema de Eugenio Beltrami. Este artículo apunta a un lector no especialista (e.g. un
estudiante de doctorado en matemática o física, etc) en geometría diferencial local.
Riferimenti bibliografici
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[Mat] V. S. Matveev, Geometric explanation of the Beltrami Theorem, Internet (2003).
[MoOl] B. Molina and C. Olmos, Manifolds all of whose flats are closed, J. Differential Geom. 45 no. 3 (1997), 575-592.
[Mil] J. Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 3 2 (1958), 215-223.
[Olm] C. Olmos, A geometric proof of Berger holonom y theorem, Ann. of Math. 161 no. 1 (2005), 579-588.
[Sp2] M. Spivak, A comprehensive Introduction to Differential Geometry, Vol. 2, 2nd ed, Perish, Inc., Berkeley, California, 1979
[Sp3] M. Spivak, A comprehensive Introduction to Differential Geometry, Vol. 3, 2nd ed, Publish or Perish, Inc., Berkeley, California, 1979.
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[Zeg] A. Zeghib, Remarks on Lorentz symmetric spaces, Compositio Math., 140 (2004), 1675-1678.
