Journal article

Locally homogeneous aspherical Sasaki manifolds

  • Baues, Oliver Department of Mathematics, University of Fribourg, Chemin du Musée 23, CH-1700 Fribourg, Switzerland
  • Kamishima, Yoshinobu Department of Mathematics, Josai University, Keyaki-dai 1-1, Sakado, Saitama 350-0295, Japan
Published in:
  • Differential Geometry and its Applications. - 2020, vol. 70, p. 101607
English 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.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
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