RIEMANNIAN GEOMETRY OF THE REAL FLAG MANIFOLD OF TYPE A 2 AND GEODESIC PROPERTIES OF A WEYL-EQUIVARIANT CELLULAR DECOMPOSITION THEREOF

Arthur Garnier (1)

1 UPJV - Université de Picardie Jules Verne

Using three-dimensional spherical space forms, Chirivi, Spreafico and the author found a cellular structure on the flag manifold SO(3)/S(O(1) 3), equivariant with respect to the action of the Weyl group W = S3. In this note, we give some Riemannian geometry properties of this decomposition.

Domaines: Géométrie différentielle [math.DG]

Arthur Garnier. RIEMANNIAN GEOMETRY OF THE REAL FLAG MANIFOLD OF TYPE A 2 AND GEODESIC PROPERTIES OF A WEYL-EQUIVARIANT CELLULAR DECOMPOSITION THEREOF. 2021. ⟨hal-03372068⟩