Riemannian foliations of the rank one symmetric spaces
HTML articles powered by AMS MathViewer
- by Richard H. Escobales
- Proc. Amer. Math. Soc. 95 (1985), 495-498
- DOI: https://doi.org/10.1090/S0002-9939-1985-0806095-7
- PDF | Request permission
Abstract:
In this paper Riemannian folfiations of spheres by spheres and of projective spaces by projective spaces of the same kind are classified by using earlier results of the author and a theorem of Ucci.References
- Richard H. Escobales Jr., Riemannian submersions with totally geodesic fibers, J. Differential Geometry 10 (1975), 253–276. MR 370423
- Richard H. Escobales Jr., Riemannian submersions from complex projective space, J. Differential Geometry 13 (1978), no. 1, 93–107. MR 520604
- Richard H. Escobales Jr., Sufficient conditions for a bundle-like foliation to admit a Riemannian submersion onto its leaf space, Proc. Amer. Math. Soc. 84 (1982), no. 2, 280–284. MR 637184, DOI 10.1090/S0002-9939-1982-0637184-5
- Alfred Gray, A note on manifolds whose holonomy group is a subgroup of $\textrm {Sp}(n)\cdot \textrm {Sp}(1)$, Michigan Math. J. 16 (1969), 125–128. MR 244913
- Robert Hermann, A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle, Proc. Amer. Math. Soc. 11 (1960), 236–242. MR 112151, DOI 10.1090/S0002-9939-1960-0112151-4
- Walter A. Poor, Differential geometric structures, McGraw-Hill Book Co., New York, 1981. MR 647949
- H. Blaine Lawson Jr., The quantitative theory of foliations, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 27, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at Washington University, St. Louis, Mo., January 6–10, 1975. MR 0448368
- Bruce L. Reinhart, Closed metric foliations, Michigan Math. J. 8 (1961), 7–9. MR 120592
- R. T. Smith, The spherical representations of groups transitive on $S^{n}$, Indiana Univ. Math. J. 24 (1974/75), 307–325. MR 364557, DOI 10.1512/iumj.1974.24.24028
- R. T. Smith, Harmonic mappings of spheres, Amer. J. Math. 97 (1975), 364–385. MR 391127, DOI 10.2307/2373717
- Jack Ucci, On the nonexistence of Riemannian submersions from $\textbf {C}\textrm {P}(7)$ and $\textrm {QP}(3)$, Proc. Amer. Math. Soc. 88 (1983), no. 4, 698–700. MR 702302, DOI 10.1090/S0002-9939-1983-0702302-8 H. Gluck, F. Warner and W. Ziller, Fibrations of spheres by parallel great spheres, Univ. of Pennsylvania Preprint. A. Ranjan, Riemannian submersions of Riemannian manifolds with connected totally geodesic fibres, Doctoral Thesis, Tata Inst. of Fundamental Research, Bombay, 1983.
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 495-498
- MSC: Primary 57R30; Secondary 53C12, 53C30
- DOI: https://doi.org/10.1090/S0002-9939-1985-0806095-7
- MathSciNet review: 806095