Duke Mathematical Journal

The Gauss equations and rigidity of isometric embeddings

Eric Berger, Robert Bryant, and Phillip Griffiths

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Article information

Source
Duke Math. J. Volume 50, Number 3 (1983), 803-892.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077303336

Mathematical Reviews number (MathSciNet)
MR714831

Zentralblatt MATH identifier
0526.53018

Digital Object Identifier
doi:10.1215/S0012-7094-83-05039-1

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53B25: Local submanifolds [See also 53C40] 58A15: Exterior differential systems (Cartan theory) 58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]

Citation

Berger, Eric; Bryant, Robert; Griffiths, Phillip. The Gauss equations and rigidity of isometric embeddings. Duke Mathematical Journal 50 (1983), no. 3, 803--892. doi:10.1215/S0012-7094-83-05039-1. http://projecteuclid.org/euclid.dmj/1077303336.


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References

  • [1] C. B. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math. 61 (1939), 633–644.
  • [2] E. Berger, R. Bryant, and P. Griffiths, Some isometric embedding and rigidity results for Riemannian manifolds, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 8, part 1, 4657–4660.
  • [3] R. Brynat, S. S. Chern, and P. Griffiths, Proceedings of the Beijing Symposium, 1980.
  • [4] R. Bryant and P. Griffiths, Characteristic varieties of exterior differential systems, to appear.
  • [5] R. Bryant, P. Griffiths, and D. Yang, Characteristics and existence of isometric embeddings, to appear.
  • [6] E. Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques, Actualités Sci. Ind., no. 994, Hermann et Cie., Paris, 1945.
  • [7] E. Cartan, Bull. Soc. Math. France 47 (1919), 125–160 and 48 (1920), 132–208.
  • [8] S. S. Chern and R. Osserman, Remarks on the Riemannian metric of a numerical submanifold, to appear.
  • [9] J. Gasqui, Sur l'existence d'immersions isométriques locales pour les variétés riemanniennes, J. Differential Geometry 10 (1975), 61–84.
  • [10] H. Goldschmidt, Existence theorems for analytic linear partial differential equations, Ann. of Math. (2) 86 (1967), 246–270.
  • [11] R. E. Greene and H. Jacobowitz, Analytic isometric embeddings, Ann. of Math. (2) 93 (1971), 189–204.
  • [12] M. Gromov and V. Rokhlin, Russian Math. Surveys 25 (1970), 1–57.
  • [13] E. Kaneda and N. Tanaka, Rigidity for isometric imbeddings, J. Math. Kyoto Univ. 18 (1978), no. 1, 1–70.
  • [14] D. E. Littlewood, The Theory of Group Characters and Matrix Representations of Groups, Oxford University Press, New York, 1940.
  • [15] J.-P. Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197–278.
  • [16] M. Spivak, A comprehensive introduction to differential geometry. Vol. V, Publish or Perish Inc., Boston, Mass., 1975.
  • [17] T. I. Thomas, Acta Math. 67 (1936), 164–211.
  • [18] J. Vilms, Local isometric imbedding of Riemannian $n$-manifolds into Euclidean $(n+1)$-space, J. Differential Geometry 12 (1977), no. 2, 197–202.
  • [19] J. Vilms, Factorization of curvature operators, Trans. Amer. Math. Soc. 260 (1980), no. 2, 595–605.
  • [20] H. Weyl, The Classical Groups, Princeton Press, 1946.