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2015•Proceedings of the American Mathematical SocietyRequires access

Some curvature pinching results for Riemannian manifolds with density

William Wylie

Open publisher page 4 citations

Abstract

In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifolds with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.

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What this paper is about

In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifolds with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifolds with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.

Key concepts: Curvature, Curvature of Riemannian manifolds, Sectional curvature, Scalar curvature, Mathematics, Ricci-flat manifold, Geology, Riemann curvature tensor

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