|
Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Retrieve article in:
PDF
Book Information
Author(s):
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:
- [Ak] T. Akahori, A new approach to the local embedding theorem of CR-structures of n ≥ 4... Mem. Amer. Math. Soc., no. 336, Amer. Math. Soc., Providence, R. I., 1987. MR 888499
- [BBG] E. Berger, R. Bryant and P. Griffiths, The Gauss equations and rigidity of isometric embeddings, Duke Math. J. 50 (1983), 800-892. MR 714831
- [BGY] R. Bryant, P. Griffiths and D. Yang, Characteristics and existence of isometric embeddings, Duke Math. J. 50 (1983), 893-994. MR 726313
- [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.
- [CC] S. S. Chern and C. Chevalley, Elie Cartan and his mathematical work, Bull. Amer. Math. Soc. 58 (1952), 217-250. MR 46972
- [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.
- [Gr] R. Greene, Isometric embeddings of Riemannian and pseudo-Riemannian manifolds, Mem. Amer. Math. Soc. no. 97, Amer. Math. Soc., Providence, R. I., 1970. MR 262980
- [Ha] R. S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N. S. ) 7 (1982), 65-222. MR 656198
- [Ho] L. Hormander, Implicit function theorems, mimeographed notes of lectures given at Stanford University, 1977.
- [Ja1] H. Jacobowitz, Extending isometric embeddings, J. Differential Geometry 9 (1974), 291-307. MR 377773
- [Ja2] H. Jacobowitz, Homogeneous solvability and CR structures, Notas de Curso, Univerśidade Pederal de Pernambuco, Recife, Brazil, 1988. MR 934571
- [JT1] H. Jacobowitz and F. Treves, Nonrealizable CR structures, Invent. Math. 66 (1982), 231-249. MR 656622
- [JT2] H. Jacobowitz and F. Treves, Abberant CR structures, Hokkaido Math. J. 12 (1983), 276-292. MR 719968
- [Ku] M. Kuranishi, Strongly pseudoconvex CR structures over small balls, Part III. An embedding theorem. Ann. of Math. (2) 116 (1982), 249-330. MR 672837
- [Li] Chang-Shou Lin, The local isometric embedding problem in R, Thesis, NYU, New York 1983.
- [Mo] J. Moser, A rapidly converging iteration method and non-linear differential equations, Ann. Scuola Norm. Sup. Pisa (3) 20 (1966), 499-535. MR 206461
- [Na] J. Nash, The embedding problem for Riemannian manifolds, Ann. of Math. (2) 63 (1956), 20-64. MR 75639
- [Ni] L. Nirenberg, On a problem of Hans Lewy, Uspekhi Mat. Nauk 292 (176) (1974), 241-251. MR 492752
- [Sc] J. Schwartz, On Nash's implicit functional theorem, Comm. Pure Appl. Math. 13 (1960), 509-530. MR 114144
- [Se] F. Sergeraert, Une generalisation du théorème des fonctiones implicites de Nash, C. R. Acad. Sci. Paris Ser. A 270 (1970), 861-863. 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.
Additional Information:
Reviewer(s):
Howard
Jacobowitz
Review Information:
Journal:
Bull. Amer. Math. Soc.
19
(1988),
498-504.
DOI:
10.1090/S0273-0979-1988-15717-5
PII:
S 0273-0979(1988)15717-5
|
Comments: webmaster@ams.org