Corrigendum to “Optimal inequalities involving Casorati curvatures along Riemannian maps and Riemannian submersions for Sasakian space forms” [J. Geom. Phys. 210 (2025) 105417] (Journal of Geometry and Physics (2025) 210, (S0393044025000014), (10.1016/j.geomphys.2025.105417))

Abstract

In Theorem 3.1, the structure vector field ξ is in the orthogonal complementary distribution to [Formula presented]. As a consequence Theorem 3.1 needs to be changed to Theorem 0.1 Let F be a Riemannian map from a Riemannian manifold [Formula presented] such that the structure vector field ξ is in [Formula presented] on the horizontal space satisfy [Formula presented] Moreover, the case of equality occurs in any of the above two inequalities at a point [Formula presented] on the horizontal space [Formula presented] satisfy [Formula presented] In the last sentence on page 4 including the equation (3.6) should be deleted because it is not used in the proof. On page 6, since the characteristic vector field ξ is in the horizontal distribution, an orthonormal basis [Formula presented]. In this reason, the characteristic vector field ξ in Theorem 4.2 should be in the horizontal distribution. As a consequence Theorem 4.2 needs to be changed to Theorem 0.2 Let F be a Riemannian submersion from a Sasakian space form [Formula presented] with the characteristic vector field ξ belongs to the horizontal distribution. Then, the normalized δ-vertical Casorati curvatures [Formula presented] for the Riemannian submersion satisfy the following optimizations: