Skip to main content
Log in

Reduction of the codimension of regular isometric immersions

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Bibliography

  1. Asperti, A.C.: Immersions of surfaces into 4-dimensional spaces with nonzero normal curvature. Ann. Mat. Pura Apl.125, 313–328 (1980)

    Google Scholar 

  2. do Carmo, M.P.: O Método do Referencial Móvel. III Latin American School of Mathematics at the Instituto Matemática Pura e Aplicada (Rio de Janeiro 1976) Rio de Janeiro: IMPR 1976

    Google Scholar 

  3. Colares, A.C., do Carmo, M.P.: On minimal immersions with parallel normal curvature tensor. In: Geometry and Topology. Proceedings of the III Latin American School of Mathematics (Rio de Janeiro 1976) pp. 104–113. Lectures notes in Mathematics597 Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  4. Chen, B.Y.: Geometry of Submanifolds. New York: Marcel Dekker 1976

    Google Scholar 

  5. Chen, B.Y., Yano, K.: Integral formulas for submanifolds and their applications. J. Differential Geometry5, 467–477 (1971)

    Google Scholar 

  6. Dajczer, M.: Reduction of the Codimension of Regular Isometric Immersions. An. Acad. Brasil. Ci.51, 597–598 (1979)

    Google Scholar 

  7. Erbacher, J.: Reduction of codimension of isometric immersions. J. Differential Geometry5, 333–340 (1971)

    Google Scholar 

  8. Itoh, T.: Minimal Surfaces in 4-dimensional Riemannian manifolds of constant curvature. Kodai Math. Sem. Rep.24, 451–458 (1972)

    Google Scholar 

  9. Kenmotsu, K.: On compact minimal surfaces with constant curvature II. Tôhoku Math. J.27, 291–301 (1975)

    Google Scholar 

  10. Lawson, B., Jr.: Complete minimal surfaces inS 3. Ann. of Math.92, 335–374 (1970)

    Google Scholar 

  11. Little, J.A. On singularities of submanifolds of higher dimensional Euclidean spaces. Ann. Mat. Pura Apl.83, 261–335 (1969)

    Google Scholar 

  12. Moore, J.D.: Isometric immersions of Space Forms. Pacific J. Math.40, 157–166 (1972)

    Google Scholar 

  13. Otsuki, T.: Isometric imbedding of Riemannian manifolds in a Riemannian manifold. J. Math. Soc. Japan6, 221–234 (1954)

    Google Scholar 

  14. Spivak, M.: A Comprehensive Introduction to Differential Geometry V, Boston: Publish or Perish 1975

    Google Scholar 

  15. Yau, S.T.: Submanifolds with constant mean curvature I. Amer. J. Math.96, 346–366 (1974)

    Google Scholar 

  16. Yau, S.T.: Submanifolds with constant mean curvature II. Amer. J. Math.97, 76–100 (1975)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dajczer, M. Reduction of the codimension of regular isometric immersions. Math Z 179, 263–286 (1982). https://doi.org/10.1007/BF01214317

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01214317

Keywords

Navigation