ARVANITOYEORGOS, Andreas, Ioannis CHRYSIKOS a Yusuke SAKANE. Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation. Journal of Symbolic Computation. Elsevier Science Ltd, 2013, roč. 55, August 2013, s. 59-71. ISSN 0747-7171. Dostupné z: https://dx.doi.org/10.1016/j.jsc.2013.03.005. |
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@article{2394733, author = {Arvanitoyeorgos, Andreas and Chrysikos, Ioannis and Sakane, Yusuke}, article_number = {August 2013}, doi = {http://dx.doi.org/10.1016/j.jsc.2013.03.005}, keywords = {Homogeneous manifold; Einstein metric; Generalized flag manifold; Algebraic system of equations; Gröbner basis; Lexicographic order}, language = {eng}, issn = {0747-7171}, journal = {Journal of Symbolic Computation}, title = {Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation}, url = {https://www.sciencedirect.com/science/article/pii/S0747717113000497}, volume = {55}, year = {2013} }
TY - JOUR ID - 2394733 AU - Arvanitoyeorgos, Andreas - Chrysikos, Ioannis - Sakane, Yusuke PY - 2013 TI - Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation JF - Journal of Symbolic Computation VL - 55 IS - August 2013 SP - 59-71 EP - 59-71 PB - Elsevier Science Ltd SN - 07477171 KW - Homogeneous manifold KW - Einstein metric KW - Generalized flag manifold KW - Algebraic system of equations KW - Gröbner basis KW - Lexicographic order UR - https://www.sciencedirect.com/science/article/pii/S0747717113000497 N2 - 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. ER -
ARVANITOYEORGOS, Andreas, Ioannis CHRYSIKOS a Yusuke SAKANE. Proving isometry for homogeneous Einstein metrics on flag manifolds by symbolic computation. \textit{Journal of Symbolic Computation}. Elsevier Science Ltd, 2013, roč.~55, August 2013, s.~59-71. ISSN~0747-7171. Dostupné z: https://dx.doi.org/10.1016/j.jsc.2013.03.005.
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