Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation

ARVANITOYEORGOS, Andreas, Ioannis CHRYSIKOS and Yusuke SAKANE. Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation. Journal of Symbolic Computation. Elsevier Science Ltd, 2013, vol. 55, August 2013, p. 59-71. ISSN 0747-7171. Available from: https://dx.doi.org/10.1016/j.jsc.2013.03.005.

Basic information

Original name

Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation

Authors

ARVANITOYEORGOS, Andreas, Ioannis CHRYSIKOS and Yusuke SAKANE

Edition

Journal of Symbolic Computation, Elsevier Science Ltd, 2013, 0747-7171

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Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.709

DOI

http://dx.doi.org/10.1016/j.jsc.2013.03.005

UT WoS

000318321800005

Keywords in English

Homogeneous manifold; Einstein metric; Generalized flag manifold; Algebraic system of equations; Gröbner basis; Lexicographic order

Tags

RIV ne

Tags

International impact, Reviewed

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Abstract

V originále

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.