Skip to main content
SpringerLink
Log in

Variational theory of Riemannian subspaces

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

If a subspace of a Riemannian manifold is varied the tensors associated with the subspace also vary. The appropriate concept of tensorial variation is introduced and the tensorial variations of several tensors are calculated. A general formula for the variation of an integral is given. Applications are made to the mean curvature integrals of hypersurfaces.

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. BERRY, T. G.: Invariant variational problems on a subspace of a Riemannian space. Tensor, N.S.25, 217–228 (1972)

    Google Scholar 

  2. REILLY, R. C.: Variational properties of functions of the mean curvatures for hypersurfaces in space forms. J. Differential Geometry8, 465–477 (1973)

    Google Scholar 

  3. RUND, H.: Integral formulae on hypersurfaces in Riemannian manifolds. Ann. Math. Pura Appl. (4),88, 92–122 (1971)

    Google Scholar 

  4. RUND, H.: Invariant theory of variational problems on subspaces of a Riemannian manifold. Hamburger Math. Einzelschriften, Neue Folge, Heft 5, Vandenhoeck & Ruprecht, Göttingen, 1971

    Google Scholar 

  5. SCHOUTEN, J. A.: Ricci-Calculus. Second Ed. Springer, Berlin, Göttingen, Heidelberg, 1954

    Google Scholar 

  6. VOSS, K.: Einige differentialgeometrische Kongruenzsätze für geschlossene Flächen und Hyperflächen. Math. Ann.131, 180–218 (1956)

    Google Scholar 

  7. WILLMORE, T. J., and JHAVERI, C. S.: An extension of a result of Bang-Yen Chen. Quarterly J. Math. Oxford Ser. 2,23, 319–323 (1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung Mathematik, Universität Dortmund, 4600, Dortmund 50, West Germany

    Moritz Armsen

Authors
  1. Moritz Armsen
    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

Armsen, M. Variational theory of Riemannian subspaces. Manuscripta Math 26, 315–329 (1978). https://doi.org/10.1007/BF01167728

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01167728

Keywords

Search

Navigation