Infinitesimal Bendings for Classes of Two Dimensional Surfaces

TL;DR

This paper investigates infinitesimal bendings of certain 2D surfaces in three-dimensional space, using advanced mathematical techniques involving differential equations and complex analysis.

Contribution

It introduces new methods for constructing bending fields by reducing the problem to solvability of specific differential equations with periodic coefficients.

Findings

Established conditions for infinitesimal bendings of surface classes.

Developed solution techniques for Bers-Vekua type equations.

Provided explicit constructions of bending fields for certain surfaces.

Abstract

Infinitesimal bendings for classes of two-dimensional surfaces in $\mathbb{R}^3$ are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers-Vekua type equations and systems of differential equations with periodic coefficients.