Skip to main content
SpringerLink
Log in

Lie transformation groups and differential geometry

  • Conference paper
  • First Online:
Differential Geometry and Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1255))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alexandrov, A. D., A characteristic property of spheres. Ann. Mat. Pura Appl. 58 (1962), 303–315.

    Article  MathSciNet  Google Scholar 

  2. Back, A., Do Carmo, M. and Hsiang, W. Y., Fundamental equations of equivariant differential geometry (Preprint, U.C. Berkeley, 1980).

    Google Scholar 

  3. Bombieri, E., De Giorgi, E. and Giusti, E., Minimal cones and the Bernstein problem, Invent. Math. 7 (1969) 243–268.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bott, R., The stable homotopy of the classical groups, Ann. of Math. 70 (1959), 313–337.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bott, R. and Samelson, H., Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1959), 964–1029.

    Article  MathSciNet  MATH  Google Scholar 

  6. Cartan, E., Sur une classe remarquable déspaces de Riemann, Bull. Soc. Math. France 54 (1926), 214–264; 55 (1927) 114–134.

    MathSciNet  MATH  Google Scholar 

  7. Cartan, É., La géométrie des groupes de transformations, J. Math. Pures Appl. 6 (1927), 1–119.

    MathSciNet  MATH  Google Scholar 

  8. Cartan, É., Sur des familles remarquables d'hypersurfaces isoparamétrique dans les espaces spheriques, Math. Z. 45 (1939) 335–367.

    Article  MathSciNet  MATH  Google Scholar 

  9. Ferus, D. and Karcher, H., Non-rotational minimal spheres and minimizing cones, Comment. Math. Helv. 60 (1985), 247–269.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ferus, D., Karcher, H. and Münzner, H. F., Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z. 177 (1981) 479–502.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hsiang, W. C. and Hsiang, W. Y., Some problems in differentiable transformation groups. Proc. of the conf. on transf. groups. New Orleans, 1967. Springer-Verlag, N.Y.

    Google Scholar 

  12. Hsiang, W. Y., Minimal cones and the spherical Bernstein problem I. Ann. of Math. 118 (1983), 61–73

    Article  MathSciNet  MATH  Google Scholar 

  13. Hsiang, W. Y., Minimal cones and the spherical Bernstein problem II. Invent. Math. 74 (1983), 351–369.

    Article  MathSciNet  MATH  Google Scholar 

  14. Hsiang, W. T., and Hsiang, W. Y., On the construction of constant mean curvature imbeddings of exotic and / or knotted spheres into Sn(1), Invent. Math. 82 (1985), 423–445.

    Article  MathSciNet  MATH  Google Scholar 

  15. Hsiang, W. T., Hsiang, W. Y. and Sterling, I., On the construction of codimension two minimal immersions of exotic spheres into euclidean spheres, Invent. Math. 82 (1985) 447–460.

    Article  MathSciNet  MATH  Google Scholar 

  16. Hsiang, W.Y., Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces, I. J. Diff. Geom. 17 (1982), 337–356.

    MathSciNet  MATH  Google Scholar 

  17. Hsiang, W. Y. and Huynh, H. L., Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces, II, (Preprint, Pam-284, U.C. Berkeley, 1985)

    Google Scholar 

  18. Hsiang, W. Y. and Sterling, I., Minimal cones and the spherical Bernstein problem, III. (to appear in Invent. Math.)

    Google Scholar 

  19. Hsiang, W. Y., On the laws of trigonometries of two point homogeneous spaces (Preprint, U. C. Berkeley)

    Google Scholar 

  20. Hsiang, W. Y., On the formula of volume of a tetrahedon in spherical or hyperbolic spaces (Preprint, U.C. Berkeley)

    Google Scholar 

  21. Hsiang, W. Y., Palais, R. S. and Terng, C. L., The topology and geometry of isoparametric submanifolds in euclidean spaces Proc. Nat. Acad. Sci. USA 82 (1985), 4863–4865.

    Article  MathSciNet  MATH  Google Scholar 

  22. Hsiang, W. Y. and Tomter, P., On minimal immersions of Sn−1 into Sn(1), n⩾4. (Preprint U.C. Berkeley)

    Google Scholar 

  23. Hsiang, W. Y. On the construction of infinitely many congruence classes of imbedded closed minimal hypersurfaces in Sn(1) for each n⩾3 (Preprint, U.C. Berkeley)

    Google Scholar 

  24. Münzner, H. F., Isoparametrische Hyperflächen in Sphären I, Math. Ann. 251 (1980), 57–71

    Article  MathSciNet  MATH  Google Scholar 

  25. Münzner, H. F., Isoparametrische Hyperflächen in Sphären II. Math. Ann. 256 (1981), 215–232.

    Article  MathSciNet  MATH  Google Scholar 

  26. Ozeki, H. and Takeuchi, M., On some types of isoparametric hypersurfaces, I, Tohoku Math. J. 27 (1975), 515–559

    Article  MATH  Google Scholar 

  27. Ozeki, H. and Takeuchi, M., On some types of isoparametric hypersurfaces, II, Tohoku Math. J. 28 (1976), 7–55.

    Article  MATH  Google Scholar 

  28. Pólya, G. and Szegö, G., Isoperimetric inequalities in mathematical physics, Ann. of Math. Studies vol. 27, Princeton University Press, Princeton, N. J.

    Google Scholar 

  29. Schmidt, E., Der Brunn-Minkowskische Satz und sein Spiegeltheorem sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und hyperbolischen Geometrie, Math. Ann. 120 (1947–49), 307–429.

    Article  MATH  Google Scholar 

  30. Wente, H. C., Counterexample to a conjecture of H. Hopf, Pacific J. Math. 121 (1986), 193–243.

    Article  MathSciNet  MATH  Google Scholar 

  31. Coxeter, H. S. M., The functions of Schläfli and Lobatschefsky, Quart. J. Math. Oxford. 6 (1935), 13–29.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of California, Berkeley

    Wu-Yi Hsiang

Authors
  1. Wu-Yi Hsiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Chaohao Gu Marcel Berger Robert L. Bryant

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Hsiang, WY. (1987). Lie transformation groups and differential geometry. In: Gu, C., Berger, M., Bryant, R.L. (eds) Differential Geometry and Differential Equations. Lecture Notes in Mathematics, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077679

Download citation

  • DOI: https://doi.org/10.1007/BFb0077679

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17849-1

  • Online ISBN: 978-3-540-47883-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation