Homogeneous Einstein Metrics on Generalized Flag Manifolds with G(2)-type T-Roots

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Authors

CHRYSIKOS Ioannis ARVANITOYEORGOS Andreas SAKANE Yusuke

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

Faculty of Science

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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