Investigation of a real algebraic surface

The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow

“…Repeating similar procedures as in the case of the curves s k and r k we can obtain parametric equations (10) of the curves l k . Clearly, l i ∩ l j = ∅ for i = j.…”

“…Since then studies related to this topic were continued in [1,3,7,22] concerning classifications of singular (equilibria) points of (4) being Einstein metrics and their bifurcations. The authors of [2,10,11] studied an interesting and quite complicated surface of bifurcations of (4) defined by a symmetric polynomial equation in three variables a 1 , a 2 , a 3 of degree 12. In the sequel authors of [4,8] considered the evolution of positively curved Riemannian metrics under the influence of ( 5) on an interesting class of generalized Wallach spaces with coincided parameters a 1 = a 2 = a 3 := a ∈ (0, 1/2) generalizing some results of [14,15].…”

On Degenerated Singular Points of Dynamical Systems Related to the Normalized Ricci Flow on Generalized Wallach Spaces

“…s 1 = a 1 + a 2 + a 3 , s 2 = a 1 a 2 + a 1 a 3 + a 2 a 3 и s 3 = a 1 a 2 a 3 . Свойства алгебраической поверхности Ω, определяемой уравнением Q(a 1 , a 2 , a 3 ) = 0, изучены в работах [8][9][10]. Поставим теперь вопрос о том, при каких (a 1 , a 2 , a 3 ) ∈ R 3 система (4) может допускать хотя бы одну особую точку, удовлетворяющую усло-О вырожденных особых точках динамических систем вию σ = δ = 0.…”

Invariant Einstein metrics on generalized Wallach spaces

“…Another proof of these theorem could be found in [6]. According to [2], we denote by O 1 , O 2 , and O 3 the components containing the points (1/6, 1/6, 1/6), (7/15, 7/15, 7/15), and (1/6, 1/4, 1/3) respectively.…”