2014/11/21 by N. A. Abiev, Abiev, N. A.
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Geometric Analysis and Curvature Flows #math.DG #msc:14P05 #msc:14Q10 #msc:34C05 #msc:37C10 #msc:53C30 #msc:53C44
paper · pdf · doi:10.48550/arxiv.1411.5814
9 pages, 4 figures, some typos corrected
arxiv created 2014/12/02 · arxiv updated 2014/12/03
We study topological structures of the sets (0,1/2)3 ∩ Ω and (0,1/2)3 ∖ Ω, where~Ω is one special algebraic surface defined by a symmetric polynomial in variables a1,a2,a3 of degree~12. These problems arise in studying of general properties of degenerate singular points of dynamical systems obtained from the normalized Ricci flow on generalized Wallach spaces. Our main goal is to prove the connectedness of (0,1/2)3 ∩ Ω and to determine the number of connected components of (0,1/2)3 ∖ Ω. Key words and phrases: Riemannian metric, generalized Wallach space, normalized Ricci flow, dynamical system, degenerate singular point of dynamical system, real algebraic surface, singular point of real algebraic surface.