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Riemannian Manifolds Isometric to a Sphere

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This article explores isometric immersions of Riemannian manifolds, revealing links to curvature properties and eigenvectors.

The study shows that if a tangential vector field is an eigenvector, the manifold is isometric to a sphere.
It provides evidence that the condition on the Ricci curvature leads to the manifold being a sphere of constant curvature.
Using Nash's embedding theorem, any Riemannian manifold can be isometrically immersed in a higher Euclidean space.
The results include both direct implications and their converses in the context of Riemannian geometry.

Suha B. Al-Shaikh (2025) studied this question.

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