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2003•Unpublished venueRequires access

On the product Riemannian manifolds

M. Atc

Open publisher page 2 citations

Abstract

In this paper, we discuss the Riemannian curvature tensor and the Riemannian- Christoel curvature tensor of a product Riemannian manifold. We show that the Riemannian curvature tensor and the Riemannian-Christoel curvature ten- sor of the product Riemannian manifold can be written respectively as the sum of the Riemannian curvature tensor and the Riemannian-Christoel curvature tensor of each Riemannian manifold. Furthermore, making use of these results some theorems regarding the local symmetry, satness and sectional curvature are given.

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What this paper is about

In this paper, we discuss the Riemannian curvature tensor and the Riemannian- Christoel curvature tensor of a product Riemannian manifold. We show that the Riemannian curvature tensor and the Riemannian-Christoel curvature ten- sor of the product Riemannian manifold can be written respectively as the sum of the Riemannian curvature tensor and the Riemannian-Christoel curvature tensor of each Riemannian manifold. Furthermore, making use of these results some theorems regarding the local symmetry, satness and sectional curvature are given.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we discuss the Riemannian curvature tensor and the Riemannian- Christoel curvature tensor of a product Riemannian manifold. We show that the Riemannian curvature tensor and the Riemannian-Christoel curvature ten- sor of the product Riemannian manifold can be written respectively as the sum of the Riemannian curvature tensor and the Riemannian-Christoel curvature tensor of each Riemannian manifold. Furthermore, making use of these results some theorems regarding the local symmetry, satness and sectional curvature are given.

Key concepts: Riemann curvature tensor, Curvature of Riemannian manifolds, Sectional curvature, Scalar curvature, Ricci curvature, Mathematics, Prescribed scalar curvature problem, Ricci decomposition

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