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DOI: 10.23671/VNC.2017.3.7257

On Topological Structure of Some Sets Related to the Normalized Ricci Flow on Generalized Wallach Spaces

Abiev N. A.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 3.
Abstract:
We study topological structures of the sets \((0,1/2)^3 \cap \Omega\) and \((0,1/2)^3 \setminus \Omega\), where \(\Omega\) is one special algebraic surface defined by a symmetric polynomial 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 \((0,1/2)^3 \cap \Omega\) and to determine the number of connected components of \((0,1/2)^3 \setminus \Omega\).
Keywords: 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
Language: English Download the full text  
For citation: Abiev N. A. On Topological Structure of Some Sets† Related to the Normalized Ricci Flow on Generalized Wallach Spaces. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 3, pp.5-13. DOI 10.23671/VNC.2017.3.7257
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