Cauchy-Riemannian Submanifold of Maximal Dimension inStatistical Sasakian Space Form

Abstract

In this paper, we study statistical Cauchy-Riemannian maximal submanifolds in the statistical Sasakian space form which naturally inherit their Sasakian structure from the ambient. We show that there exists a Cauchy-Riemann maximal submanifold in statistical Sasakian space form where the $\psi$-holomorphic sectional curvature of the ambient space is bounded. Moreover, a Cauchy-Riemannian maximal submanifold in the statistical Sasakian space form has at most four principal curvatures under some properties of second fundamental form $C$ and its dual.