Homogeneous Einstein metrics on the generalized flag manifold Sp(n)/(U(p) x U(n-p))

Andreas Arvanitoyeorgos; Ioannis Chrysikos; Yusuke Sakane

Homogeneous Einstein metrics on the generalized flag manifold Sp(n)/(U(p) x U(n-p))

Differential Geometry 2017-01-10 v1

Authors: Andreas Arvanitoyeorgos , Ioannis Chrysikos , Yusuke Sakane

Abstract

We find the precise number of non-K\"ahler $Sp(n)$ -invariant Einstein metrics on the generalized flag manifold $M=Sp(n)/(U(p)\times U(n-p))$ with $n\geq 3$ and $1\leq p\leq n-1$ . We use an analysis on parametric systems of polynomial equations and we give some insight towards the study of such systems.

Keywords

homogeneous Einstein metrics generalized flag manifolds Sp(n) non-Kähler metrics parametric polynomial systems

Cite

@article{arxiv.1010.4472,
  title  = {Homogeneous Einstein metrics on the generalized flag manifold Sp(n)/(U(p) x U(n-p))},
  author = {Andreas Arvanitoyeorgos and Ioannis Chrysikos and Yusuke Sakane},
  journal= {arXiv preprint arXiv:1010.4472},
  year   = {2017}
}

Comments

15 pages

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