Generic submanifolds of manifolds equipped with a Kenmotsu 3-structure (Q2771171)

In 1970, Y.-Y. Kuo introduced the notion of an almost contact metric 3-structure on a manifold \(M\) of dimension \(4m+3\). It consists of three almost contact metric structures such that the structure tensors satisfy some specific conditions. If these structures are all three of Sasakian type, then \(M\) is called a 3-Sasakian manifold and these spaces have been studied intensively during the recent past. In case the three structures are of Kenmotsu type, then \(M\) is said to be a 3-Kenmotsu manifold. The theory of hypersurfaces and general submanifolds has already been studied for 3-Sasakian manifolds, in particular by A. Bejancu.NEWLINENEWLINENEWLINEAfter their study of hypersurfaces of 3-Kenmotsu manifolds, the authors now treat the case of generic submanifolds \(N\) which are tangent to the three characteristic vector fields. They mainly focus on the integrability conditions for several distributions which are naturally defined on \(M\) and on some aspects of the extrinsic geometry of their maximal integral submanifolds.