Journal of Differential Geometry

Minimal submanifolds of low cohomogeneity

Wu-yi Hsiang and H. Blaine Lawson, Jr.

Full-text: Open access

Article information

Source
J. Differential Geom. Volume 5, Number 1-2 (1971), 1-38.

Dates
First available in Project Euclid: 25 June 2008

Permanent link to this document
http://projecteuclid.org/euclid.jdg/1214429775

Mathematical Reviews number (MathSciNet)
MR0298593

Zentralblatt MATH identifier
0219.53045

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]

Citation

Hsiang, Wu-yi; Lawson, Jr., H. Blaine. Minimal submanifolds of low cohomogeneity. J. Differential Geom. 5 (1971), no. 1-2, 1--38. http://projecteuclid.org/euclid.jdg/1214429775.


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References

  • [1] E. Bombieri, E. De Giorgi and E. Giusti, Minimal cones and the Bernstein problem, Invent. Math, 7 (1969) 243-268.
  • [2] P. Byrd and M. Friedman, Handbook of elliptic integrals for engineers and physicists, Springer, Berlin, 1954.
  • [3] S. Chern, S. Kobayashi, and M. do Carmo, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional analysis and related fields, Proc. Conf. in Honor of Marshall Stone, Springer, Berlin, 1970.
  • [4] R. Courant, Calculus of variations, Lecture notes, New York University, 1946.
  • [5] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
  • [6] W. C. Hsiang and W. Y. Hsiang, Differentiate actions of compact, connected classical groups. I, Amer. J. Math. 89 (1967) 705-786.
  • [7] W. C. Hsiang and W. Y. Hsiang, Differentiate actions of compact, connected classical groups. II, to appear.
  • [8] W. Y. Hsiang, On the compact, homogeneous minimal submanifolds, Proc. Nat. Acad. Sci. U.S.A. 56 (1966) 5-6.
  • [9] W. Y. Hsiang, On the compact, Remarks on closed minimal submanifolds in the standard Riemannian m-sphere, J. Differential Geometry 1(1967) 257-267.
  • [10] W. Y. Hsiang, On the compact, A survey on regularity theorems in differentiable, compact transformation groups, Proc. Conf. on Transformation Groups, Springer, Berlin, 1968.
  • [11] S. Kobayashi and N. Nomizu, Foundations of differential geometry, Vol. II, Interscience, New York, 1969.
  • [12] H. B. Lawson, Jr., Local rigidity theorems for minimal hypersurfaces, Ann. of Math. 89 (1969) 187-197.
  • [13] H. B. Lawson, Jr., Complete minimal surfaces in S8, Ann. of Math. 90 (1970), 335-374.
  • [14]H. B. Lawson, Jr., Rigidity theorems in rank-X symmetric spaces, J. Differential Geometry 4 (1970) 349-357.
  • [15] H. B. Lawson, Jr., The equivariant Plateau problem and interior regularity, to appear.
  • [16] J. Milnor, Morse theory, Ann. of Math. Studies, No. 51, Princeton University Press, Princeton, 1963.
  • [17] S. Myers and N. Steenrod, The group of isometries of a Riemannian manifold, Ann. of Math. 40 (1939) 400.
  • [18] D. Montgomery and H. Samelson, Transformation groups of spheres, Ann. of Math. 44 (1943) 454-470.
  • [19] D. Montgomery, H. Samelson and C. T. Yang, Exceptional orbits of highest dimension, Ann. of Math. 64 (1956) 131-141.
  • [20] D. Montgomery and C. T. Yang, The existence of a slice, Ann. of Math. 65 (1957) 108-116.
  • [21] G. D. Mostow, Equivariant imbeddings in Euclidean spaces, Ann. of Math. 65 (1957) 432-446.
  • [22] B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966) 459-469.
  • [23] T. Otsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970) 145-173.
  • [24] J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math. 88 (1968) 62-105.