Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-08T11:27:07.641Z Has data issue: false hasContentIssue false

Rigidity for elliptic isometric imbeddings

Published online by Cambridge University Press:  22 January 2016

Noboru Tanaka*
Affiliation:
Kyoto University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The main purpose of the present paper is to give the details of the results announced in the P. J. A. note [11], establishing some global theorems on rigidity for a certain class of isometric imbeddings.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Adams, J. F., Lax, P. D. and Phillips, R. S., On matrices whose real linear combinations are non-singular, Proc. Amer. Math. Soc., 16 (1965), 318322.Google Scholar
[2] Cartan, E., Sur la possibilité de plonger un espace riemannien donné dans un espace euclidien, Ann. Soc. Pol. Math., 6 (1927), 117.Google Scholar
[3] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry I, Inter science Publishers, New York, 1963; II, 1969.Google Scholar
[4] Kodaira, K. and Spencer, D. C., On deformations of complex analytic structures III, Ann. Math., 71 (1960), 4376.CrossRefGoogle Scholar
[5] Lichnerowicz, A., Géométrie des Groupes de Transformations, Dunod, Paris, 1958.Google Scholar
[6] Nash, J. F., The imbedding problem for Riemannian manifolds, Ann. Math., 63 (1956), 2063.CrossRefGoogle Scholar
[7] Nirenberg, L., The Weyl and Minkowski problems in the differential geometry in the large, Comm. Pure and Appl. Math., 6 (1953), 337394.CrossRefGoogle Scholar
[8] Quillen, D. G., Formal properties of over-determined systems of linear partial differential equations, Ph. D. thesis, Harvard University, 1964.Google Scholar
[9] Singer, I. M. and Sternberg, S., The infinite group of Lie and Cartan, J. Analyse Math., 15 (1965), 1114.CrossRefGoogle Scholar
[10] Shiga, K. and Sunada, R., The Hodge Decomposition in Elliptic Complexes, Seminar Reports of Global Analysis, Tokyo Institute of Technology, 1971 (in Japanese).Google Scholar
[11] Tanaka, N., Rigidity for elliptic isometric imbeddings, Proc. Japan Acad., 48 (1972), 370372.Google Scholar
[12] Yano, K., Differential Geometry on Complex and Almost Complex Spaces, Pergamon Press, New York, 1965.Google Scholar