JournalsjemsVol. 28, No. 3pp. 1353–1386

A Smale–Barden manifold admitting K-contact but not Sasakian structure

A Smale–Barden manifold admitting K-contact but not Sasakian structure cover
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Abstract

We give the first example of a simply connected compact -manifold (Smale–Barden manifold) which admits a K-contact structure but does not admit any Sasakian structure, settling a long-standing question of Boyer and Galicki.

Cite this article

Vicente Muñoz, A Smale–Barden manifold admitting K-contact but not Sasakian structure. J. Eur. Math. Soc. 28 (2026), no. 3, pp. 1353–1386

DOI 10.4171/JEMS/1496