Skip to Main Content

Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


MathSciNet review: 1567709
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Phillip A. Griffiths and Gary R. Jensen
Title: Differential systems and isometric embeddings
Additional book information: Annals of Mathematics Studies, vol. 114, Princeton University Press, Princeton, N. J., 1987, xii+225 pp., $35.00 (cloth). $15.00 (paper). ISBN 0-691-08429-7.

References [Enhancements On Off] (What's this?)

  • Takao Akahori, A new approach to the local embedding theorem of CR-structures for $n\geq 4$ (the local solvability for the operator $\overline \partial _b$ in the abstract sense), Mem. Amer. Math. Soc. 67 (1987), no. 366, xvi+257. MR 888499, DOI 10.1090/memo/0366
  • Eric Berger, Robert Bryant, and Phillip Griffiths, The Gauss equations and rigidity of isometric embeddings, Duke Math. J. 50 (1983), no. 3, 803–892. MR 714831, DOI 10.1215/S0012-7094-83-05039-1
  • Robert L. Bryant, Phillip A. Griffiths, and Deane Yang, Characteristics and existence of isometric embeddings, Duke Math. J. 50 (1983), no. 4, 893–994. MR 726313, DOI 10.1215/S0012-7094-83-05040-8
  • [Br] R. Bryant, S. S. Chern, R. Gardner, H. Goldschmidt, P. Griffiths and D. Yang, Essays on exterior differential systems (in preparation).

    [Bu] C. Burstin, Ein Beitragzum Problem der Einbettung der Riemannschen Raume in Euklidishen Raume, Math. Sb. 38 (1931), 74-85.

  • Shiing-Shen Chern and Claude Chevalley, Obituary: Elie Cartan and his mathematical work, Bull. Amer. Math. Soc. 58 (1952), 217–250. MR 46972, DOI 10.1090/S0002-9904-1952-09588-4
  • [Ea] M. Eastwood, The Hill-Penrose-Sparling C.R.-folds, Twistor Newsletter 18 (1984), 16.

    [Go] E. Goursat, Leçons sur le probleme de Pfaff, Gauthier-Villars, Paris, 1922.

  • Robert E. Greene, Isometric embeddings of Riemannian and pseudo-Riemannian manifolds. , Memoirs of the American Mathematical Society, No. 97, American Mathematical Society, Providence, R.I., 1970. MR 0262980
  • Richard S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 1, 65–222. MR 656198, DOI 10.1090/S0273-0979-1982-15004-2
  • [Ho] L. Hormander, Implicit function theorems, mimeographed notes of lectures given at Stanford University, 1977.

  • H. Jacobowitz, Extending isometric embeddings, J. Differential Geometry 9 (1974), 291–307. MR 377773
  • Howard Jacobowitz, Homogeneous solvability and CR structures, Notas de Curso [Course Notes], vol. 25, Universidade Federal de Pernambuco, Departamento de Matemática, Recife, 1988. MR 934571
  • Howard Jacobowitz and François Trèves, Nonrealizable CR structures, Invent. Math. 66 (1982), no. 2, 231–249. MR 656622, DOI 10.1007/BF01389393
  • Howard Jacobowitz and François Trèves, Aberrant CR structures, Hokkaido Math. J. 12 (1983), no. 3, 276–292. MR 719968, DOI 10.14492/hokmj/1470081006
  • Masatake Kuranishi, Strongly pseudoconvex CR structures over small balls. I. An a priori estimate, Ann. of Math. (2) 115 (1982), no. 3, 451–500. MR 657236, DOI 10.2307/2007010
  • [Li] Chang-Shou Lin, The local isometric embedding problem in R, Thesis, NYU, New York 1983.

  • Jürgen Moser, A rapidly convergent iteration method and non-linear differential equations. II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 20 (1966), 499–535. MR 206461
  • John Nash, The imbedding problem for Riemannian manifolds, Ann. of Math. (2) 63 (1956), 20–63. MR 75639, DOI 10.2307/1969989
  • L. Nirenberg, A certain problem of Hans Lewy, Uspehi Mat. Nauk 29 (1974), no. 2(176), 241–251 (Russian). Translated from the English by Ju. V. Egorov; Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. MR 0492752
  • J. Schwartz, On Nash’s implicit functional theorem, Comm. Pure Appl. Math. 13 (1960), 509–530. MR 114144, DOI 10.1002/cpa.3160130311
  • Francis Sergeraert, Une généralisation du théorème des fonctions implicites de Nash, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A861–A863 (French). MR 259699
  • [Sp] M. Spivak, Differential geometry, Volume 5, Publish or Perish, Boston, 1975.

    [We] J. Weingarten, Über die Theorie der aufeinander abwickelbaren Oberflachen, Berlin, 1884.

    [Wy] H. Weyl, Cartan on groups and differential geometry, Bull. Amer. Math. Soc. 44 (1938), 598-601.

    [Ya] D. Yang, Involutive hyperbolic differential systems, thesis, Harvard Univ., Cambridge, Mass., 1982.


    Review Information:

    Reviewer: Howard Jacobowitz
    Journal: Bull. Amer. Math. Soc. 19 (1988), 498-504
    DOI: https://doi.org/10.1090/S0273-0979-1988-15717-5