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

TL;DR

This paper constructs nontrivial infinitesimal bendings for certain 2D surfaces with positive curvature and planar points, demonstrating their nonrigidity, which advances understanding of surface flexibility under specific geometric conditions.

Contribution

It introduces a method to construct infinitesimal bendings for a class of surfaces with positive curvature and planar points, establishing their nonrigidity.

Findings

Existence of nontrivial infinitesimal bendings for the surfaces.

Surfaces are shown to be nonrigid under the given conditions.

The results apply to orientable, compact surfaces with boundary and specific curvature properties.

Abstract

Nontrivial infinitesimal bendings for a class of two-dimensional surfaces are constructed. The surfaces considered here are orientable; compact; with boundary; have positive curvature everywhere except at finitely many planar points; and have vanishing first homology group.As a consequence, a nonrigidity result for such surfaces is deduced.