Submetries vs. submersions
Luis
Guijarro
and
Gerard
Walschap
Source: Rev. Mat. Iberoamericana Volume 27, Number 2
(2011), 605-619.
Abstract
We study submetries between Alexandrov spaces and show how some of the usual features of Riemannian submersions fail due to the lack of smoothness.
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1307713039
Zentralblatt MATH identifier: 05936703
Mathematical Reviews number (MathSciNet): MR2848532
References
Berestovskii, V.: “Submetries” of three-dimensional forms of nonnegative curvature. Sibirsk. Mat. Zh. 28 (1987), no. 4, 44-56 (Russian). Siberian Math. J. 28 (1987), no. 4, 552-562 (English traslation).
Mathematical Reviews (MathSciNet): MR906032
Berestovskii, V. and Guijarro, L.: A metric characterization of Riemannian submersions. Ann. Global Anal. Geom. 18 (2000), no. 6, 577-588.
Mathematical Reviews (MathSciNet): MR1800594
Digital Object Identifier: doi:10.1023/A:1006683922481
Burago, D., Burago, Y. and Ivanov, S.: A course in metric geometry. Graduate Studies in Mathematics 33. American Mathematical Society, Providence, RI, 2001.
Mathematical Reviews (MathSciNet): MR1835418
Zentralblatt MATH: 0981.51016
Guijarro, L. and Petersen, P.: Rigidity in non-negative curvature. Ann. Sci. École Norm. Sup. (4) 30 (1997), no. 5, 595-603.
Mathematical Reviews (MathSciNet): MR1474806
Zentralblatt MATH: 1008.53042
Digital Object Identifier: doi:10.1016/S0012-9593(97)89933-8
Hermann, R.: A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle. Proc. Amer. Math. Soc. 11 (1960), 236-242.
Mathematical Reviews (MathSciNet): MR112151
Zentralblatt MATH: 0112.13701
Digital Object Identifier: doi:10.1090/S0002-9939-1960-0112151-4
JSTOR: links.jstor.org
Lang, U. and Schroeder, V.: Kirszbraun's theorem and metric spaces of bounded curvature. Geom. Funct. Anal. 7 (1997), 535-560.
Mathematical Reviews (MathSciNet): MR1466337
Zentralblatt MATH: 0891.53046
Digital Object Identifier: doi:10.1007/s000390050018
Lytchak, A.: Open map theorem for metric spaces. Algebra i Analiz 17 (2005), no. 3, 139-159. Translation in St. Petersburg Math. J. 17 (2006), no. 3, 477-491.
Mathematical Reviews (MathSciNet): MR2167848
Lytchak, A.: Submetrien von Alexandrov-Räumen. Part of the PhD. Thesis, available at: http://www.math.uni-bonn.de/people/lytchak/publications.html.
Perelman, G.: Alexandrov spaces with a lower curvature bound, II. Unpublished preprint.
Perelman, G. and Petrunin, A.: Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem. Algebra i Analiz 5 (1993), no. 1, 242-256 (Russian). Translation in St. Petersburg Math. J. 5 (1994), no. 1, 215-227.
Mathematical Reviews (MathSciNet): MR1220499
Petrunin, A.: Application of quasigeodesics and gradient curves. In Comparison geometry (Berkeley, CA, 1993-94), 203-219. Math. Sci. Res. Inst. Publ. 30. Cambridge Univ. Press, Cambridge, 1997.
Mathematical Reviews (MathSciNet): MR1452875
Zentralblatt MATH: 0892.53026
Petrunin, A.: Semiconcave functions in Alexandrov's geometry. In Surveys in differential geometry. Vol. XI, 137-201. Surv. Differ. Geom. 11. Int. Press, Somerville, MA, 2007.
Mathematical Reviews (MathSciNet): MR2408266
Zentralblatt MATH: 1166.53001
Walschap, G.: Metric foliations and curvature. J. Geom. Anal. 2 (1992), no. 4, 373-381.
Mathematical Reviews (MathSciNet): MR1170481
Zentralblatt MATH: 0769.53021
Wilking, B.: A duality theorem for Riemannian foliations in nonnegative sectional curvature. Geom. Funct. Anal. 17 (2007), no. 4, 1297-1320.
Mathematical Reviews (MathSciNet): MR2373019
Zentralblatt MATH: 1139.53014
Digital Object Identifier: doi:10.1007/s00039-007-0620-0
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