Gauge-compatible tensors on statistical manifolds: splitting and submanifold geometry

Mirjana Milijevic, Luis P. Yapu

We study statistical manifolds $(M,g,\nabla ,{\nabla }^{\ast })$ endowed with a nonzero $(1,1)$-tensor field $\Theta$ satisfying the gauge equation \[ \nabla_X(ΘY)=Θ(\nabla_X^{*}Y). \] We first…