Einstein metrics on even-dimensional homogeneous spaces admitting a homogeneous Riemannian metric of positive sectional curvature

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

“…The recent paper [37] by Wilking and Ziller gives a new and short proof of the classification of homogeneous manifolds of positive curvature. A detailed exposition of various results on the set of invariant metrics with positive sectional curvature, the best pinching constant, and full connected isometry groups could be found in the papers [28][29][30][31][32][33][34][35].…”

Invariant Einstein metrics on three-locally-symmetric spaces

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In this paper, we classify three-locally-symmetric spaces for a connected, compact and simple Lie group. Furthermore, we give the classification of invariant Einstein metrics on these spaces.are obtained in [30], on the Kähler C-spacesare classified in [20], another approach toThe existence is proved in [26] of at least one invariant Einstein metric for every three-locally-symmetric space. Furthermore in [23], the classification of invariant Einstein metrics is given for Sp(l + m + n)/Sp(l) × Sp(m) × Sp(m) and SO(l + m + n)/SO(l) × SO(m) × SO(m).

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The Ricci Flow on Some Generalized Wallach Spaces

“…These spaces (known as Wallach spaces) are interesting because they admit invariant Riemannian metrics of positive sectional curvature (see [26]). The invariant Einstein metrics on SU (3)/T max were classified in [8] and, on the remaining two spaces, in [23]. In each of the cases, there exist exactly four invariant Einstein metrics (up to proportionality).…”

“…Solving this equations together (and taking into account the equations ( 23)) we get the following four families of solutions of (23), that include solutions under the conditions b i > 0…”