Infinitesimal Sliding Bendings of Compact Surfaces and Euler's Conjecture

We give some historical information about Euler's conjecture on the rigidityof compact surfaces as well as the available results related to its proof.We thoroughly describe an approach tothe conjecture by infinitesimal bendingsin the case when the deformation of the surface is considered in the class ofsliding bendings. We prove that Euler's conjecture is true for the surfaces ofrevolution of genus 0 in the class of sliding bendings.