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

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International Electronic Journal of Geometry
Volume:15 Issue:2
The de Rham Cohomology Group of a Hemi-Slant Submanifold in Metallic Riemannian Manifolds

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

Pages : 242-252

View : 52 | Download : 10

Publication Date : 2022-10-31

Article Type : Research Paper

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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