Curvature Relations for Lagrangian Submersions From Globally Conformal Kaehler Manifolds

Year 2025, Volume: 3 Issue: 1, 20 - 33, 24.06.2025

Beran Pirinççi

Abstract

In this paper, we derive curvature identities for Lagrangian submersions from globally conformal Kaehler manifolds onto Rieman nian manifolds. Then, we give a relation between the horizontal lift of the curvature tensor of the base manifold and the curvature tensor of a fiber. We examine the necessary and sufficient conditions for the total manifolds of Lagrangian submersions to be Einstein. We also obtain Ricci, scalar, sectional, holomorphic bisectional and holomorphic sectional curvatures for these submer sions. Finally, we give some inequalities involving the scalar and Ricci curvatures, and we also provide Chen-Ricci inequality for Lagrangian submersions from globally conformal Kaehler space forms.

Keywords

Riemannian submersion , Lagrangian submersion , globally conformal Kaehler manifold , Chen-Ricci inequality

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