Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms

In this paper, we obtain the upper bounds for the normalized [Formula: see text]-Casorati curvatures and generalized normalized [Formula: see text]-Casorati curvatures for statistical submanifolds in Sasaki-like statistical manifolds with constant curvature. Further, we discuss the equality case of the inequalities. Moreover, we give the necessary and sufficient condition for a Sasaki-like statistical manifold to be [Formula: see text]-Einstein. Finally, we provide the condition under which the metric of Sasaki-like statistical manifolds with constant curvature is a solution of vacuum Einstein field equations.