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

• Autoři: CHRYSIKOS Ioannis; ARVANITOYEORGOS Andreas; SAKANE Yusuke
• Rok publikování: 2013
• Druh: Článek ve sborníku
• Konference: Prospects of Differential Geometry and Its Related Fields Proceedings of the 3rd International Colloquium on Differential Geometry and Its Related Fields
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://www.worldscientific.com/doi/abs/10.1142/9789814541817_0002
• Doi: http://dx.doi.org/10.1142/9789814541817_0002
• Obor: Obecná matematika
• Klíčová slova: Homogeneous Einstein metric Generalized flag manifold Riemannian submersion Grobner basis
• Popis: 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.

Související projekty

• Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku