The aim of this paper is to show that a compact quaternion-Kähler manifolds which is acted on isometrically by a compact Lie group G with a hypersurface orbit is a symmetric space. This result, already proved by A. Dancer and A. Swann for G semisimple, is now completed in the reductive case.
A note on quaternion-Kähler manifolds / L. VERDIANI; F. PODESTA'. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - STAMPA. - 11:(2000), pp. 279-283. [10.1142/S0129167X00000143]
A note on quaternion-Kähler manifolds
VERDIANI, LUIGI;PODESTA', FABIO
2000
Abstract
The aim of this paper is to show that a compact quaternion-Kähler manifolds which is acted on isometrically by a compact Lie group G with a hypersurface orbit is a symmetric space. This result, already proved by A. Dancer and A. Swann for G semisimple, is now completed in the reductive case.
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