Metallic Structures on Product Manifolds and Chen-Ricci Inequalities

Year 2024, Volume: 17 Issue: 2, 660 - 678, 27.10.2024

Mustafa Gök

https://doi.org/10.36890/iejg.1458491

Abstract

In this study, we discuss metallic structures on product manifolds and derive the Chen-Ricci inequalities for remarkable submanifolds determined by the behaviour of their tangent bundles with regard to the action of the metallic structure in a locally decomposable metallic Riemannian manifold whose components are spaces of constant curvature. Moreover, the equality cases are considered in order to characterize these submanifolds.

Keywords

Metallic structure, metallic Riemannian manifold, Riemannian submanifold, real space form, Ricci curvature, $k$-Ricci curvature, Chen-Ricci inequality

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