Statistical Submersions with Parallel Almost Complex Structures

The aim of the present paper is to study statistical submersions with parallel almost complex structures. First, we define the notion of the generalized Kähler-like statistical submersion and give examples of the Kähler-like statistical submersions. In addition, we investigate total space and fibers under certain conditions. After, we introduce some results on J-invariant, \(J^{*}\) $J^{\ast }$ -invariant and anti-invariant generalized Kähler-like statistical submersions.