Invariant Einstein Metrics on Certain Homogeneous Spaces

Invariant Einstein metrics on flag manifolds with four isotropy summands

“…In this case, the scale invariants are functions of the parameter . By computing these for the two non-Kähler-Einstein metrics given in (33) we conclude that these metrics are non-isometric. The Kähler-Einstein metrics Finally, let M = G/K be a generalized flag manifold of Type IIb, and let g = (x 1 ,x 2 ,x 3 ,x 4 ) be a G-invariant metric on M. In this case the scalar curvature is given by…”

New Einstein–Randers metrics on some homogeneous manifolds

“…, [17]). Let be a compact connected semi-simple Lie group endowed with the left-invariant metric ⟨, ⟩ given by (2.1).…”

Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$

“…In [13], Park-Sakane computed the Ricci tensor in a similar way. In their formula appears the dimension d i of each irreducible submodules m i , while (equivalently) the equation (5) depends on the amounts of factors U (n i ) in the isotropy subgroup K. Actually Park-Sakane formula is very useful when one wants to describe the Ricci tensor on homogeneous spaces with few isotropy summands or maximal flag manifolds (see for example [18], [3] [14]).…”