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

中文翻译：

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紧致曲面的无穷小滑动弯曲与欧拉猜想

我们提供了有关欧拉紧致曲面刚性猜想的一些历史信息以及与其证明相关的可用结果。我们彻底描述了在滑动弯曲类中考虑表面变形的情况下通过无穷小弯曲进行猜想的方法。我们证明了欧拉猜想对于滑动弯曲类中的亏格 0 旋转曲面是正确的。