The de Rham Cohomology Group of a Hemi-Slant Submanifold in Metallic Riemannian Manifolds

Year 2022, Volume: 15 Issue: 2, 242 - 252, 31.10.2022

Mustafa Gök

https://doi.org/10.36890/iejg.1118628

Cited By: 2

Abstract

In this study, we answer the question under what conditions a hemi-slant submanifold of locally decomposable metallic Riemannian manifolds admits a well defined canonical de Rham cohomology class. Firstly, we give the integrability and minimality conditions of the distributions arose from its definition. Later, we find some necessary conditions depending on the above-named concepts of the associated distributions for such a type of submanifold to define a de Rham cohomology class. Furthermore, we analyzed the non-triviality of this cohomology class In the end, we construct two examples which enable better expressing the main results.

Keywords

De Rham cohomology group, metallic Riemannian manifold, hemi-slant submanifold, Riemannian submanifold

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