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Totally flat foliations and peakless functions

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References

  1. V. Bangert, Totally convex sets in complete Riemannian manifolds. J. Diff. Geom.16, 333–345 (1981).

    Google Scholar 

  2. R. L. Bishop andB. O'Neill, Manifolds of negative curvature. Trans. Amer. Math. Soc.145, 1–49 (1969).

    Google Scholar 

  3. H.Busemann, The geometry of geodesics. New York 1955.

  4. H. Busemann andB. B. Phadke, Peakless and monotone functions onG-spaces. Tsukuba J. Math.7 (1), 105–135 (1983).

    Google Scholar 

  5. J. Cheeger andD. Gromoll, On the structure of complete manifolds of nonnegative curvature. Ann. Math.96, 413–443 (1972).

    Google Scholar 

  6. J. Cheeger andD. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature. J. Diff. Geom.6, 119–128 (1971).

    Google Scholar 

  7. R. E. Greene andK. Shiohama, Convex functions on complete noncompact manifolds: Topological structure. Invent. Math.63, 129–157 (1981).

    Google Scholar 

  8. R. Ichida, Riemannian manifolds with compact boundary. Yokohama Math. J.29, 169–177 (1981).

    Google Scholar 

  9. N. Innami, A classification of BusemannG-surfaces which possess convex functions. Acta Math.148, 15–29 (1982).

    Google Scholar 

  10. N. Innami, Splitting theorems of Riemannian manifolds. Compositio Math.47, 237–247 (1982).

    Google Scholar 

  11. N.Innami, Convexity in Riemannian manifolds without focal points, (in press).

  12. D. L. Johnson andL. B. Whitt, Totally geodesic foliations. J. Diff. Geom.15, 225–235 (1980).

    Google Scholar 

  13. S. Kashiwabara, The decomposition of a differentiable manifold and its applications. Tôhoku Math. J.11, 43–53 (1959).

    Google Scholar 

  14. A. Kasue, Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary. J. Math. Soc. Japan35, 117–131 (1983).

    Google Scholar 

  15. G.Oshikiri, Totally geodesic foliations and Killing fields. Preprint.

  16. V. A. Toponogov, Spaces with straight lines. Amer. Math. Soc. Transl.37, 278–280 (1964).

    Google Scholar 

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Innami, N. Totally flat foliations and peakless functions. Arch. Math 41, 464–471 (1983). https://doi.org/10.1007/BF01207575

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  • DOI: https://doi.org/10.1007/BF01207575

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