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TitleProving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation
Author(s) Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane
TypeArticle in Journal
AbstractAbstract The question whether two Riemannian metrics on a certain manifold are isometric is a fundamental and also a challenging problem in differential geometry. In this paper we ask whether two non-Kähler homogeneous Einstein metrics on a certain flag manifold are isometric. We tackle this question by reformulating it into a related question on a parametric system of polynomial equations and answering it by carefully combining Gröbner bases and geometrical arguments. Using this technique, we are able to prove the isometry of such metrics.
KeywordsHomogeneous manifold, Einstein metric, Generalized flag manifold, Algebraic system of equations, Gröbner basis, Lexicographic order
URL http://www.sciencedirect.com/science/article/pii/S0747717113000497
JournalJournal of Symbolic Computation
Pages59 - 71
Translation No
Refereed No