Parallelism in \(K\)-contact geometry
It is proved that on a \(K\)-contact manifold \(M\), there are no non-zero parallel differential \(p\)-forms for \(1\leqslant p\leqslant 2n\), where \(\dim M=2n+1\). This is a generalization of a result by \textit{D.\ E.\ Blair} and \textit{S.\ I.\ Goldberg} stating that compact Sasakian manifolds do not admit such forms [J. Differ. Geom. 1, 347--354 (1967; Zbl 0163.43902)].
scientific article; zbMATH DE number 6121643