Motion of Charged Particles and Homogeneous Geodesics in Kähler $C$-Spaces with Two Isotropy Summands

Invariant Einstein metrics on flag manifolds with four isotropy summands

“…Then U/K = U /K [10, p. 179]. In our case, the fibers U /K are the spaces SO (9) (10), and E 7 /SU (7) × U (1), respectively. These are generalized flag manifolds with two isotropy summands (see [8]), so we can easily compute the triples (c 4 22 ) for the spaces U /K .…”

“…We define the function ht : → Z, ht(α i ) = m i . In [9] the authors classified all generalized flag manifolds M = G/K with two isotropy summands. This was done by painting black in the Dynkin diagram ( ) of G a simple root of height 2, that is, [27] Kimura obtained all flag manifolds with three isotropy summands, by setting…”

“…where c 3 (9), each real submodule m i associated to the positive t-root ξ i can be expressed in terms of root vectors E ±α (α ∈ R + M ) such that κ(α) = ξ i . Therefore, from (6) (3) we obtain (30).…”

Equigeodesics on Generalized Flag Manifolds with Two Isotropy Summands

“…According to [2] and [3], a generalized flag manifolds has two isotropy summands if, and only if, Π K = Π − {α i0 } such that the simple root has Table 1. Generalized flag manifolds with two isotropy summands…”

Equigeodesics on Generalized Flag Manifolds with b 2 (G / K) = 1

“…Table 3 for the generalized flag manifold E 7 /SU (5)× U (1) × SU (2). In particular, all vectors in these subspaces are structural equigeodesic vectors.…”