## On Sasaki spaces and equidistant Kähler spaces.(English. Russian original)Zbl 0631.53018

Sov. Math., Dokl. 34, 428-431 (1987); translation from Dokl. Akad. Nauk SSSR 291, 33-36 (1986).
A Riemannian space V is said to be equidistant [N. S. Sinyukov, Geodesic mappings of Riemannian spaces (Russian) (Nauka Moscow, 1979)], if it admits a vector field $$\xi$$ whose covariant derivative is of the form $$\nabla \xi =\rho I$$, where $$\rho$$ is a function on V and I is the identity (1,1)-tensor field. The author finds the local shape of the metric of an equidistant Kähler space with $$\rho\neq 0$$. Some consequences for the metric of a Sasaki space are also discussed.
Reviewer: Z.Olszak

### MSC:

 53B35 Local differential geometry of Hermitian and Kählerian structures

### Keywords:

equidistant Kähler space; Sasaki space