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TitleHomogeneous Einstein metrics on generalized flag manifolds $mathrmSp(n)/(mathrm U(p) timesmathrm U(q) timesmathrmSp(n-p-q))$.
Author(s) Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe construct the Einstein equation for an invariant Riemannian metric on generalized flag manifolds Sp(n)/(U(p) × U(q) × Sp(n-p-q)). By computing a Gröbner basis for a system of polynomials on six variables, we prove that the generalized flag manifolds Sp(3)/(U(1) × U(1) × Sp(1)), Sp(4)/(U(1) × U(1) × Sp(2)) and Sp(4)/(U(2) × U(1) × Sp(1)) admit exactly three, six and two non-Kähler invariant Einstein metrics up to isometry, respectively.

Keywords Homogeneous Einstein metric; Generalized flag manifold; Gröbner basis
ISBN978-981-4355-46-9/hbk; 978-981
URL http://www.worldscientific.com/doi/10.1142/9789814355476_0001
PublisherHackensack, NJ: World Scientific
Translation No
Refereed No