Abstract:
In this paper we study infinitesimal deformations of convex pieces of surfaces with boundary. It is assumed that the surface has positive gaussian curvature $K>0$. We investigate infinitesimal deformations, subject on the boundary of the surface to the condition $\lambda\delta k_n+\mu\delta\tau_g=\sigma$, where $\delta k_n$ and $\sigma\tau_g$ are variations of the normal curvature and geodesic torsion of the boundary, $\lambda$ and $\mu$ are fixed known functions, and $\sigma$ an arbitrary given function. We establish necessary and sufficient conditions for the rigidity of the surface under these boundary conditions.
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