A real variety with boundary and its global parameterization. (English. Russian original) Zbl 1455.53075

Batkhin, A. B.

Program. Comput. Softw. 43, No. 2, 75-83 (2017); translation from Programmirovanie 43, No. 2, 17-27 (2017).

Summary: An algebraic variety in \(R^3\) 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.

MSC:

53C30	Differential geometry of homogeneous manifolds
13P15	Solving polynomial systems; resultants
13P10	Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14P05	Real algebraic sets
53E20	Ricci flows
14Q10	Computational aspects of algebraic surfaces

Software:

PGeomlib; desing

References:

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