Publication details
Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Symbolic Computation |
| Citation | |
| web | https://www.sciencedirect.com/science/article/pii/S0747717113000497 |
| Doi | https://doi.org/10.1016/j.jsc.2013.03.005 |
| Keywords | Homogeneous manifold; Einstein metric; Generalized flag manifold; Algebraic system of equations; Gröbner basis; Lexicographic order |
| Description | 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. |