On contact \(p\)-spheres (Q2485444)

The author considers a geometrical structure called \textit{contact \(p\)-sphere}, previously introduced by H. Geiges and J. Gonzalo, i.e., a family of contact forms parametrized by the \(p\)-sphere. The main results are some existence theorems for such a structure. Some interesting examples where this structure can be naturally recognized are given also. In particular, it is proved that if a manifold of dimension \(4n-1\) admits a Sasakian \(3\)-structure given by three forms \(\omega_i\), \(i=1,2,3\), then these forms generate a (round and taut) contact sphere.