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An example relevant to curvature pinching theorems for Riemannian foliations

Author: James J. Hebda
Journal: Proc. Amer. Math. Soc. 114 (1992), 195-199
MSC: Primary 53C12; Secondary 53C20, 57R30
MathSciNet review: 1086327
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Abstract: We describe a one-parameter family of codimension-$ 2$ Riemannian foliations of $ {S^3}$ which are not transversely homogeneous. The example shows that the comparison theorem for Riemannian foliations of Kamber-Ruh-Tondeur [4] fails without an additional hypothesis.

References [Enhancements On Off] (What's this?)

  • [1] R. A. Blumenthal, Transversely homogeneous foliations, Ann. Inst. Fourier (Grenoble) 29 (1979), 143-158. MR 558593 (81h:57011)
  • [2] J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam and New York, 1975. MR 0458335 (56:16538)
  • [3] F. W. Kamber, E. A. Ruh, and P. Tondeur, Almost transversely symmetric foliations (Proc. 2nd Internat. Sympos. on Differential Geometry, Pensicola 1985), Lecture Notes in Math., vol. 1209, Springer Verlag, Berlin and New York, 1986, pp. 184-189. MR 863756 (87k:53070)
  • [4] -, Comparing Riemannian foliations with transversely symmetric foliations, J. Differential Geom. 27 (1988), 461-475; erratum, J. Differential Geom. 32 (1990), 917. MR 940114 (89h:53079)
  • [5] P. Tondeur, The mean curvature of Riemannian foliations, Feuilletages riémanniens, quantification géométrique et mécanique (Lyon, 1986) Hermann, Paris, 1988. MR 938306 (89d:53071)

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Article copyright: © Copyright 1992 American Mathematical Society

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