Nonrigidity of a class of two dimensional surfaces with positive curvature and planar points

Meziani, A.

doi:10.1090/S0002-9939-2013-11488-7

Nonrigidity of a class of two dimensional surfaces with positive curvature and planar points
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Proc. Amer. Math. Soc. 141 (2013), 2137-2143 Request permission

Abstract:

Existence of nontrivial infinitesimal bendings is established for an orientable surface with boundary $S\subset \mathbb {R}^3$ that has positive curvature except at finitely many planar points and such that $H_1(S)=0$. As an application, we show that any neighborhood of such a surface $S$ (for the $C^k$ topology) contains isometric surfaces that are noncongruent.

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