the analytic solutions of the string motion, we can calculate the energy-momentum tensor easily. Then, we can study the gravitational field yielded by the stationary rotating strings, especially gravitational wave emission. It is important to clarify the property of the gravitational waves from the stationary rotating strings for verification of their existence in the universe. We will report this issue in near future[@WGE2].

It is also interesting problem to construct all cohomogeneity-one string in Minkowski[@IshiharaKozaki; @KKImink], de Sitter, and anti-de Sitter[@KKIads] spacetimes. Furthermore, it would be challenging work to find the general solutions of stationary rotating strings in the black hole spacetimes as an extended work of ref.[@FSZH].

Acknowledgments {#acknowledgments .unnumbered}
===============

We would like to thank K. Nakao and C.-M. Yoo for useful discussions. HN is supported by a JSPS Research Fellowship for Young Scientists, No. 5919. He is also supported by JSPS for Research Abroad and in part by the NSF through grants PHY-0722315, PHY-0701566, PHY-0714388, and PHY-0722703, and from grant NASA 07-ATFP07-0158.

Potential in Two-dimensions
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We consider a particle in the two-dimensional flat space driven by a potential force. In general, every metric of two-dimensional space is written in conformal flat form. The metric is written 