Warped product submanifolds of a Kenmotsu manifold (Q2911331)

Semi-slant submanifolds of almost Hermitian manifolds were introduced by \textit{N. Papaghiuc} [An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 40, No. 1, 55--61 (1994; Zbl 0847.53012)]. Let \(\widetilde u\) be an almost contact metric manifold of Kenmotsu type. In this paper, the authors investigate a class of warped product semi-slant manifolds of the types \(M= N_T\times_\lambda N_\theta\) and \(M= N_\perp\times_\lambda N_\theta\) of a Kenmotsu manifold. Let \((N_1,g_1)\), \((N_2,g_2)\) be Riemannian minifolds and \(\lambda\) a positive differentiable function on \(N_1\). The warped product is defined by \(N_1\times\lambda N_2= (N_1\times N_2, g)\), where \(g= g_1+ \lambda^2 g_2\). Let \(\overline\nabla\) be the Levi-Cività connection of \(g\), and \(\xi\) a special vector field.NEWLINENEWLINE The authors prove the following theorem: Let \(M= N_T\times_\lambda N_\theta\) be a warped product semi-slant submanifold of a Kenmotsu manifold \(\widetilde M\) such that \(\xi\in TN_T\). Then \((\overline\nabla_X F)Z\in\mu\) for which \(X\in TN_T\) and \(Z\in TN_\theta\), where \(\mu\) is an invariant normal subbundle of \(TM\)''. \(TM\) denotes the tangent bundle of \(M\), and \(F\) is a tensor field. Finally, the authors construct an example.