### Abstract

In the presence of certain symmetry, called cohomogeneity-one symmetry, the equation of motion of an extended object in spacetime reduces to the problem of finding geodesics on a certain orbit space. We present a general method for obtaining solutions of such extented objects and classifying them. The classification is carried out in 4-dimensional Minkowski space and in 5-dimensional anti-de Sitter space. The solvability condition is described in terms of Killing vectors and Killing tensors which mutually commute. In 4-dimensional Minkowski space, it is found that all types of cohomogeneity-one strings are solvable. In the case of 5-dimensional de Sitter space, there are not enough number of commuting Killing vectors but that the problem reduces to that of finding curves on a two-dimensional surface.

Original language | English |
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Title of host publication | Proceedings of Science |

Publication status | Published - 2008 |

Event | Black Holes in General Relativity and String Theory, BHs, GR and Strings 2008 - Veli Losinj, Croatia Duration: 2008 Aug 24 → 2008 Aug 30 |

### Other

Other | Black Holes in General Relativity and String Theory, BHs, GR and Strings 2008 |
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Country | Croatia |

City | Veli Losinj |

Period | 08/8/24 → 08/8/30 |

### Fingerprint

### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of Science*

**Systematic method for solving strings having a symmetry in the space-time.** / Koike, Tatsuhiko; Ishihara, Hideki; Kozaki, Hiroshi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of Science.*Black Holes in General Relativity and String Theory, BHs, GR and Strings 2008, Veli Losinj, Croatia, 08/8/24.

}

TY - GEN

T1 - Systematic method for solving strings having a symmetry in the space-time

AU - Koike, Tatsuhiko

AU - Ishihara, Hideki

AU - Kozaki, Hiroshi

PY - 2008

Y1 - 2008

N2 - In the presence of certain symmetry, called cohomogeneity-one symmetry, the equation of motion of an extended object in spacetime reduces to the problem of finding geodesics on a certain orbit space. We present a general method for obtaining solutions of such extented objects and classifying them. The classification is carried out in 4-dimensional Minkowski space and in 5-dimensional anti-de Sitter space. The solvability condition is described in terms of Killing vectors and Killing tensors which mutually commute. In 4-dimensional Minkowski space, it is found that all types of cohomogeneity-one strings are solvable. In the case of 5-dimensional de Sitter space, there are not enough number of commuting Killing vectors but that the problem reduces to that of finding curves on a two-dimensional surface.

AB - In the presence of certain symmetry, called cohomogeneity-one symmetry, the equation of motion of an extended object in spacetime reduces to the problem of finding geodesics on a certain orbit space. We present a general method for obtaining solutions of such extented objects and classifying them. The classification is carried out in 4-dimensional Minkowski space and in 5-dimensional anti-de Sitter space. The solvability condition is described in terms of Killing vectors and Killing tensors which mutually commute. In 4-dimensional Minkowski space, it is found that all types of cohomogeneity-one strings are solvable. In the case of 5-dimensional de Sitter space, there are not enough number of commuting Killing vectors but that the problem reduces to that of finding curves on a two-dimensional surface.

UR - http://www.scopus.com/inward/record.url?scp=84893041255&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893041255&partnerID=8YFLogxK

M3 - Conference contribution

BT - Proceedings of Science

ER -