Hineva and Chen-Ricci Inequalities for Ricci Curvature of Submanifolds of Product Generalized Sasakian Space Forms

Key Points

• The aim is to derive inequalities for Ricci curvature in submanifolds of product generalized Sasakian space forms.
• Derivation of sectional, Ricci, and scalar curvature for product generalized Sasakian space forms.
• Establishment of Chen-Ricci and Hineva inequalities for these submanifolds.
• Discussion of equality cases in the established inequalities.
• Chen-Ricci and Hineva inequalities are successfully established for the defined submanifolds.
• The relationships between sectional curvature and Ricci curvature are elucidated in the context of these inequalities.
• Specific cases such as product Sasakian, product cosymplectic, and product Kenmotsu space forms are explored.