On infinitesimal isometric deformations
HTML articles powered by AMS MathViewer
- by Keti Tenenblat PDF
- Proc. Amer. Math. Soc. 75 (1979), 269-275 Request permission
Abstract:
We consider an analytic n-dimensional submanifold M of the Euclidean space ${E^N}$, where $N = n(n + 1)/2$, and we prove the existence of analytic, nontrivial, infinitesimal isometric deformations, in a neighborhood of any point of M, which admits a nonasymptotic tangent hyperplane.References
- Carl B. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math. 61 (1939), 633–644. MR 170, DOI 10.2307/2371317
- E. Cartan, La déformation des hypersurfaces dans l’espace euclidien réel à $n$ dimensions, Bull. Soc. Math. France 44 (1916), 65–99 (French). MR 1504750
- Howard Jacobowitz, Deformations leaving a hypersurface fixed, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 343–351. MR 0338939
- Keti Tenenblat, A rigidity theorem for three-dimensional submanifolds in Euclidean six-space, J. Differential Geometry 14 (1979), no. 2, 187–203. MR 587547
- Keti Tenenblat, On characteristic hypersurfaces of submanifolds in Euclidean space, Pacific J. Math. 74 (1978), no. 2, 507–517. MR 494646
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 269-275
- MSC: Primary 53B25
- DOI: https://doi.org/10.1090/S0002-9939-1979-0532149-6
- MathSciNet review: 532149