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One-dimensional metric foliations on the Heisenberg group


Author: Marius Munteanu
Journal: Proc. Amer. Math. Soc. 134 (2006), 1791-1802
MSC (2000): Primary 53C12; Secondary 22E25, 57R30
DOI: https://doi.org/10.1090/S0002-9939-05-08160-8
Published electronically: October 28, 2005
MathSciNet review: 2207495
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the one-dimensional metric foliations on the $ (2n+1)$-dimensional Heisenberg group equipped with a left invariant metric are homogeneous.


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  • [1] P. Eberlein, Geometry of 2-Step Nilpotent Lie Groups with a Left Invariant Metric, Ann. scient. Éc. Norm. Sup. $ 4^{e}$ série, t. 27 (1994), 611-660. MR 1296558 (95m:53059)
  • [2] D. Gromoll and K. Grove, One-Dimensional Metric Foliations on Constant Curvature Spaces, Differential Geometry and Complex Analysis, Springer-Verlag, Berlin, Heidelberg (1985), 165-168. MR 0780042 (86b:53026)
  • [3] D. Gromoll and G. Walschap, Metric Fibrations on Euclidean Spaces, Asian J. Math 1 (1997), 716-728. MR 1621572 (99b:53041)
  • [4] D. Gromoll and G. Walschap, The Metric Fibrations of Euclidean Spaces, J. Differential Geometry 57 (2001), 233-238. MR 1879226 (2002k:53053)
  • [5] C. Jang and K. Park, Conjugate Points on 2-Step Nilpotent Groups, Geom. Dedicata 78 (2000), 65-80. MR 1742200 (2001c:53067)
  • [6] B. O'Neill, The Fundamental Equations of a Submersion, Michigan Math. J. 13 (1966), 459-469. MR 0200865 (34:751)
  • [7] B. O'Neill, Submersions and Geodesics, Duke. Math. J. 34 (1967), 363-373. MR 0216432 (35:7265)
  • [8] P. Tondeur, Foliations on Riemannian manifolds, Springer-Verlag, New York (1988). MR 0934020 (89e:53052)
  • [9] G. Walschap, Cut and Conjugate Loci in Two-Step Nilpotent Lie Groups, J. Geom. Anal. 7 (1997), 343-355. MR 1646788 (99m:53094)
  • [10] G. Walschap, Geometric Vector Fields on Lie Groups, Diff. Geom. Appl. 7 (1997), 219-230. MR 1480535 (98g:53048)
  • [11] G. Walschap, Umbilic foliations and curvature, Illinois J. Math. 41 (1997), 122-128. MR 1433190 (97m:53053)

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Additional Information

Marius Munteanu
Affiliation: Department of Mathematics, Computer Science and Statistics, SUNY College at Oneonta, Oneonta, New York 13820
Email: munteam@oneonta.edu

DOI: https://doi.org/10.1090/S0002-9939-05-08160-8
Received by editor(s): December 15, 2003
Received by editor(s) in revised form: December 31, 2004
Published electronically: October 28, 2005
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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