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A geometrical obstruction to the existence of two totally umbilical complementary foliations in compact manifolds

  • V. Non-Linear Systems, Integrability And Foliations
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References

  1. Carreras, F.J.: "Linear invariants of Riemannian almost-product manifolds", Math.Proc.Camb.Phil.Soc., 91 (1982), 99–106

    Article  MathSciNet  MATH  Google Scholar 

  2. Eells, J., Lemaire, L.: "A report on harmonic maps". Bull. London Math.Soc., 10 (1978), 1–68

    Article  MathSciNet  MATH  Google Scholar 

  3. Eells, J., Lemaire, L.: "Selected topics in harmonic maps". C.B.M.S. Regional conference series of the National Science Foundation, (1981)

    Google Scholar 

  4. Gil Medrano, O.: "Ciertas propiedades geometricas y topologicas en algunas clases de variedades riemannianas casi-producto", Tesis doctoral. Publicaciones del Departamento de Geometria y Topología no. 7, Universidad de Valencia, (1981)

    Google Scholar 

  5. Gil Medrano, O.: "On the geometric properties of some classes of almost-product structures", Rendi conti Circ. Mat. di Palermo, (preprint)

    Google Scholar 

  6. Kobayashi, S., Nomizu, K.: "Foundations in differential geometry", Interscience Publ. vol. I, II, (1962), (1969)

    Google Scholar 

  7. Mszdidjo, s. Y.: "Vector bundle valued harmonic forms and immersions of Riemannian manifolds", Csaka J. Math. 8 (1971), 1–13

    MathSciNet  Google Scholar 

  8. Miquel, V.: "Some examples of Riemannian almost-product manifolds", Pacific J. of Math. (preprint)

    Google Scholar 

  9. Montesinos, A.: "On certain classes of almost-product structures", Michigan Math. J. 30 (1983)

    Google Scholar 

  10. Naveira, A.M.: "Variedades foliadas con metrica casi-fibrada". Collect. Math., 21 (1970), 1–61

    MathSciNet  Google Scholar 

  11. Naveira, A.M.: "A classification of Riemannian almost-product manifolds", Rendi Conti di Mat. Roma, (preprint)

    Google Scholar 

  12. Poor, A.W.: "Differential geometric structures", McGraw-Hill Book Company, (1981)

    Google Scholar 

  13. Reinhart, B.L.: "Foliated manifold with bundle-like metrics", Annals of Math. 69 (1959), 119–132

    Article  MathSciNet  MATH  Google Scholar 

  14. Reinhart, B.L.: "Foliations and second fundamental forms", Proc. of the IV Intern. Colloquium on Diff. Geom. Santiago de Compostela, (1978), 246–253

    Google Scholar 

  15. Reinhart, B.L.: "Differential Geometry of Foliations", Ergebnisse der Mathematik, Springer-Verlag (1983)

    Google Scholar 

  16. Tachibana, S.: "On a characterization of Riemannian spaces admitting minimal subspaces complementary orthogonal", Nat. Sci. Rep. Ochanomizu University, 22 (1971), 85–89

    MathSciNet  MATH  Google Scholar 

  17. Vidal, E., Vidal-Costa, E.: "Special Connections and almost foliated metrics", J. Diff. Geom. 8 (1973), 297–304.

    MathSciNet  MATH  Google Scholar 

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Heinz-Dietrich Doebner Jörg-Dieter Hennig

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© 1985 Springer-Verlag

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Naveira, A.M., Rocamora, A.H. (1985). A geometrical obstruction to the existence of two totally umbilical complementary foliations in compact manifolds. In: Doebner, HD., Hennig, JD. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 1139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074589

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  • DOI: https://doi.org/10.1007/BFb0074589

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15666-6

  • Online ISBN: 978-3-540-39585-0

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