Title | **Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation** |

Author(s) | Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane |

Type | Article in Journal |

Abstract | Abstract The question whether two Riemannian metrics on a certain manifold are isometric is a fundamental and also a challenging problem in differential geometry. In this paper we ask whether two non-Kähler homogeneous Einstein metrics on a certain flag manifold are isometric. We tackle this question by reformulating it into a related question on a parametric system of polynomial equations and answering it by carefully combining Gröbner bases and geometrical arguments. Using this technique, we are able to prove the isometry of such metrics. |

Keywords | Homogeneous manifold, Einstein metric, Generalized flag manifold, Algebraic system of equations, Gröbner basis, Lexicographic order |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717113000497 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 55 |

Number | 0 |

Pages | 59 - 71 |

Year | 2013 |

Edition | 0 |

Translation |
No |

Refereed |
No |