Adapted complex structures and Riemannian homogeneous spaces

Róbert Szőke

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The spectra and the symmetric structure on a compact symmetric space.

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Quaternionic-Kähler geometry and almost Kähler A-manifolds

Włodzimierz Jelonek (2000)

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A property of Wallach's flag manifolds

Teresa Arias-Marco (2007)

Archivum Mathematicum

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In this note we study the Ledger conditions on the families of flag manifold $(M^{6} = S U (3) / S U (1) \times S U (1) \times S U (1), g_{(c_{1}, c_{2}, c_{3})})$ , $(M^{12} = S p (3) / S U (2) \times S U (2) \times S U (2), g_{(c_{1}, c_{2}, c_{3})})$ , constructed by N. R. Wallach in (Wallach, N. R., Compact homogeneous Riemannian manifols with strictly positive curvature, Ann. of Math. 96 (1972), 276–293.). In both cases, we conclude that every member of the both families of Riemannian flag manifolds is a D’Atri space if and only if it is naturally reductive. Therefore, we finish the study of $M^{6}$ made by D’Atri and Nickerson in (D’Atri, J. E., Nickerson,...