Skip to main content
SpringerLink
Log in

Immersions of cohomogeneity one Riemannian manifolds

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

This work deals with positively curved compact Riemannian manifolds which are acted on by a closed Lie group of isometries whose principal orbits have codimension one and are isotropy irreducible homogeneous spaces. For such manifolds we can show that their universal covering manifold may be isometrically immersed as a hypersurface of revolution in an euclidean space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alekseevsky, D. V.: Riemannian manifolds of cohomogeneity one. Colloq. Math. Soc. Bolyai56, 9–22 (1989).

    Google Scholar 

  2. Alekseevsky, A. V., Alekseevsky, D. V.:G-manifolds with one dimensional orbit space. Adv. in Sov. Math.20, 1–31 (1992).

    Google Scholar 

  3. Alekseevsky, A. V., Alekseevsky, D. V.: RiemannianG-manifolds with one dimensional orbit space. Ann. Glob. Anal. and Geom.11, 197–211 (1993).

    Google Scholar 

  4. Bredon, G. E.: Introduction to Compact Transformation Groups. New York: Academic Press. 1972.

    Google Scholar 

  5. Bryant, R., Salamon, S. M.: On the construction of some complete metrics with exceptional holonomy. Duke Math. J.58, 829–850 (1985).

    Google Scholar 

  6. Heinz, E.: On Weyl's embedding problem. J. Math. Mech.11, 421–454 (1962).

    Google Scholar 

  7. Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, Vol. I, II. New York: Wiley-Interscience. 1963, 1969.

    Google Scholar 

  8. Mostert, P. S.: On a compact Lie group action on manifolds. Ann. of Math.65, 447–455 (1957).

    Google Scholar 

  9. Palais, R. S., Terng, Ch. L.: A general theory of canonical forms. Trans. Amer. Math. Soc.300, 771–789 (1987).

    Google Scholar 

  10. Podestà, F., Spiro, A.: Cohomogeneity one hypersurfaces of the euclidean space. Ann. Global Analysis and Geometry13, 169–184 (1995).

    Google Scholar 

  11. Searle, C.: Cohomogeneity and positive curvature in low dimensions. Math. Z.214, 491–498 (1993).

    Google Scholar 

  12. Thomas, T. Y.: Riemann Spaces of Class one and their characterization. Acta Math.67, 169–211 (1935)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of Parma, V. M. D'Azeglio 85, Parma, Italy

    Fabio Podestà

Authors
  1. Fabio Podestà
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Podestà, F. Immersions of cohomogeneity one Riemannian manifolds. Monatshefte für Mathematik 122, 215–225 (1996). https://doi.org/10.1007/BF01320185

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01320185

1991 Mathematics Subject Classification

Key words

Search

Navigation