The Ricci flow on generalized Wallach spaces

Abstract

We consider the asymptotic behavior of the normalized Ricci flow on generalized Wallach spaces that could be considered as special planar dynamical systems. All non symmetric generalized Wallach spaces can be naturally parametrized by three positive numbers $a_1,a_2,a_3$. Our interest is to determine the type of singularity of all singular points of the normalized Ricci flow on all such spaces. Our main result gives a qualitative answer for almost all points $(a_1,a_2,a_3)$ in the cube $(0,1/2]\times (0,1/2]\times (0,1/2]$.

18 pages, 3 figures, comments are welcome

References in corpus (2)

• The Ricci flow approach to homogeneous Einstein metrics on flag manifolds
• The Ricci flow on generalized Wallach spaces

Cited by in corpus (4)

• Classification of generalized Wallach spaces
• The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow
• The Ricci flow on generalized Wallach spaces
• Invariant Einstein metrics on generalized Wallach spaces