String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension constant. A rescaled slow worldsheet time $T=\epsilon\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H
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机译：基于包括较小比例的张力常数参数的作用函数，研究了弯曲时空中的弦动力学。引入了重新定标的慢世界表时间$ T = \ epsilon \ tau $，并推导了一般的协变非线性字符串方程。结果表明，在ε展开的一阶中，这些方程式被简化为测地线导数的已知方程式，但由字符串振荡项进行了补充。这些方程针对de Sitter空间和Friedmann -Robertson-Walker空间进行求解。发现主要的弦约束被分为扰动约束链，并证明了它们的守恒性和一致性。可以确定，在拟议的微扰方法实现中，对于大哈勃常数$ H，de Sitter空间中的弦动力学是稳定的
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