In this paper, we investigate partially totally real (PTR) submanifolds of complex space forms and establish two sharp inequalities involving the normalized scalar curvature and the generalized normalized -Casorati curvatures. By using the orthogonal decomposition of the tangent bundle induced by the PTR structure and applying the Gauss equation, we derive optimal Casorati-type inequalities. Moreover, we completely characterize the equality cases in terms of invariantly quasi-umbilical submanifolds with a flat normal connection, thereby providing precise geometric interpretations of the results obtained.
Polat et al. (Tue,) studied this question.