On a Sequence of Slant Submanifolds in Almost Product Riemannian Setting

Abstract

We prove that the property of being pointwise slant is transitive on a class of proper pointwise slant submanifolds of almost product Riemannian manifolds, and illustrate this fact with an example. For a given almost product Riemannian manifold $(M_1,g,\varphi_1)$, we consider a sequence of pointwise slant submanifolds $(M_{i+1}\hookrightarrow M_i)_{i\in \mathbb{N}^*}$, and we explicitly determine the relation between the slant functions. Moreover, we state this result in a more general case.