Homogeneous Einstein Metrics on Generalized Flag Manifolds with G(2)-type T-Roots
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Proceedings |
| Conference | Prospects of Differential Geometry and Its Related Fields Proceedings of the 3rd International Colloquium on Differential Geometry and Its Related Fields |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.worldscientific.com/doi/abs/10.1142/9789814541817_0002 |
| Doi | http://dx.doi.org/10.1142/9789814541817_0002 |
| Field | General mathematics |
| Keywords | Homogeneous Einstein metric Generalized flag manifold Riemannian submersion Grobner basis |
| Description | We construct the Einstein equation for an invariant Riemannian metric on generalized flag manifolds G/K with G2-type t-roots. By computing a Gr¨obner basis for a system of polynomials on six variables, we prove that such a generalized flag manifold G/K, which is not the full flag manifold G2/T, admits exactly one invariant Kahler Einstein metric and six non Kahler invariant Einstein metrics up to isometry and scalar. |
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