Curvature invariants of Lagrangian Riemannian submersions from locally product spaces

Key Points

• The aim is to derive inequalities relating to Ricci and scalar curvatures in Lagrangian Riemannian submersions.
• Defined Lagrangian Riemannian submersions from locally product spaces onto a Riemannian manifold.
• Derived various inequalities involving horizontal and vertical distributions.
• Obtained the Chen-Ricci inequality for the Riemannian submersion.
• Established new inequalities involving Ricci and scalar curvatures.
• Demonstrated a specific non-trivial example of a Lagrangian Riemannian submersion.