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A real variety with boundary and its global parameterization

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Abstract

An algebraic variety in R3 is studied that plays an important role in the investigation of the normalized Ricci flow on generalized Wallach spaces related to invariant Einstein metrics. A procedure for obtaining a global parametric representation of this variety is described, which is based on the use of the intersection of this variety with the discriminant set of an auxiliary cubic polynomial as the axis of parameterization. For this purpose, elimination theory and computer algebra are used. Three different parameterization of the variety are obtained; each of them is valid for certain noncritical values of one of the parameters.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia

    A. B. Batkhin

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  1. A. B. Batkhin
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Correspondence to A. B. Batkhin.

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Original Russian Text © A.B. Batkhin, 2017, published in Programmirovanie, 2017, Vol. 43, No. 2.

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Batkhin, A.B. A real variety with boundary and its global parameterization. Program Comput Soft 43, 75–83 (2017). https://doi.org/10.1134/S0361768817020037

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