Baues, Oliver Kamishima, Yoshinobu 2020-06-01 Let G/H be a contractible homogeneous Sasaki manifold. A compact locally homogeneous aspherical Sasaki manifold Γ\G/H is by definition a quotient of G/H by a discrete uniform subgroup Γ≤G. We show that a compact locally homogeneous aspherical Sasaki manifold is always quasi-regular, that is, Γ\G/H is an S1-Seifert bundle over a locally homogeneous aspherical Kähler orbifold. We discuss the structure of the isometry group Isom(G/H) for a Sasaki metric of G/H in relation with the pseudo-Hermitian group Psh(G/H) for the Sasaki structure of G/H. We show that a Sasaki Lie group G, when Γ\G is a compact locally homogeneous aspherical Sasaki manifold, is either the universal covering group of SL(2,R) or a modification of a Heisenberg nilpotent Lie group with its natural Sasaki structure. We also show that any compact regular aspherical Sasaki manifold with solvable fundamental group is finitely covered by a Heisenberg manifold and its Sasaki structure may be deformed to a locally homogeneous one. In addition, we classify all aspherical Sasaki homogeneous spaces for semisimple Lie groups. application/pdf https://folia.unifr.ch/global/documents/308712 https://folia.unifr.ch/documents/308712/files/bau_lha.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.difgeo.2020.101607 info:eu-repo/semantics/openAccess License undefined Differential Geometry and its Applications. - 2020, vol. 70, p. 101607 info:eu-repo/classification/udc/51 Locally homogeneous aspherical Sasaki manifolds http://purl.org/coar/resource_type/c_6501