Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds (Q2873179)

The authors introduce the notions of semi-slant and bi-slant submanifolds of an almost contact 3-structure manifold. They prove that these notions generalize the concept of semi-slant and bi-slant submanifolds in almost contact manifolds. For instance, they generalize Theorem 5.1 in [\textit{J. L. Cabrerizo} et al., Geom. Dedicata 78, No. 2, 183--199 (1999; Zbl 0944.53028)] by saying that a submanifold of an almost metric 3-structure manifold \((\overline{M}, \xi_{i}, \eta_{i}, \phi_{i}, g)_{i=1,2,3}\), tangent to the structure vector fields \(\xi_{i}\), is 3-semi-slant if and only if there exists \(\lambda\in[-1,0)\) such that for \(i,j=1,2,3\),NEWLINENEWLINE (a) \(\mathcal{D}=\{X\in\Gamma(T M)\setminus \langle\xi_{1}, \xi_{2}, \xi_{3}\rangle: T_{i}T_{j}X=\lambda X \}\) is a distribution;NEWLINENEWLINE (b) For any \(X\in\Gamma(T M)\), orthogonal to \(\mathcal{D}\), \(N_{i}X=0\).NEWLINENEWLINE Here, \(T_{i}X\) and \(N_{i}X\) are the tangential and normal component of \(\phi_{i}X\), respectively.