Harmonic maps and s-regular manifolds. (English) Zbl 0699.53058

Sekigawa, K.; Vanhecke, L.

Čas. Pěstování Mat. 114, No. 4, 391-398 (1989).

In a previous paper by the second author, C. T. J. Dodson and M. E. Vazques-Abal [C. R. Math. Acad. Sci., Soc. R. Can. 9, 231-235 (1987; Zbl 0631.53013)], the following result has been proved: A Riemannian manifold is locally symmetric if and only if all local geodesic symmetries are harmonic maps. An analogous result is now proved for the broader class of Riemannian manifolds admitting “generalized” local symmetries (which are not necessarily involutive). This generalization is far from being routine.

Reviewer: O.Kowalski

MSC:

53C35

Differential geometry of symmetric spaces

Keywords:

generalized symmetric space; harmonic maps; local symmetries

Citations:

Zbl 0631.53013