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


53B35 Local differential geometry of Hermitian and Kählerian structures