Spaces with volume-preserving symmetries and related classes of Riemannian manifolds. (English) Zbl 0631.53033

Kowalski, Oldřich

Differential geometry on homogeneous spaces, Conf. Torino/Italy 1983, Rend. Semin. Mat., Torino, Fasc. Spec., 131-158 (1983).

[For the entire collection see Zbl 0624.00013.]
An explicit classification of all 3-dimensional (simply connected and complete) Riemannian manifolds with volume-preserving local geodesic symmetries is given. Some related classes of Riemannian manifolds are discussed in this context, namely the harmonic spaces, the naturally reductive spaces, the Riemannian homogeneous spaces on which all invariant differential operators commute, and the Riemannian manifolds on which every two random steps commute.

MSC:

53C20	Global Riemannian geometry, including pinching
53C30	Differential geometry of homogeneous manifolds
53C35	Differential geometry of symmetric spaces

Keywords:

D’Atri spaces; random walks on manifolds; volume-preserving local geodesic symmetries; harmonic spaces; reductive spaces; homogeneous spaces; invariant differential operators

Citations:

Zbl 0624.00013