General Chen's first inequality and applications for Riemannian maps

2025/10/12 by Singh, Ravindra, Meena, Kiran, Meena, Kapish Chand · 1 citation
#53B20 #53B35 #53C15 #53D15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.10505

Abstract

In this paper, we present a general form of Chen's first inequality (in short, CFI) for Riemannian maps between Riemannian manifolds. Further, using this general form, we obtain the CFI for Riemannian maps when target spaces are generalized complex and generalized Sasakian space forms. Consequently, we also obtain the CFI for Riemannian maps when the target spaces are real, complex, real Kähler, Sasakian, Kenmotsu, cosymplectic, and almost C(α) space forms. Moreover, we also discuss geometric applications of CFI on generalized complex and generalized Sasakian space forms. Specifically, we give estimations for δ-invariants within various hypotheses.

Citations

• General Casorati inequalities and implications for Riemannian maps and Riemannian submersions
• A basic inequality for submanifolds in a cosymplectic space form

Cited by

• Clairaut semi-slant/hemi-slant Riemannian maps to Kähler manifolds

Related

• General Chen-Ricci inequalities for Riemannian submersions and Riemannian maps
• On a Riemannian invariant of Chen type
• First Chen Inequality for General Warped Product Submanifolds of a Riemannian Space Form and Applications
• General Casorati inequalities and implications for Riemannian maps and Riemannian submersions
• Chen's inequality for C-totally real submanifolds in a generalized (κ,μ)-space form