Ricci Curvature and Gauss Maps of Minimal Submanifolds
Richard Atkins
TL;DR
This paper investigates how Ricci curvature influences the properties of minimal submanifolds in Euclidean space and spheres, focusing on the behavior of their Gauss maps as bounded embeddings.
Contribution
It establishes new conditions on Ricci curvature that ensure the Gauss map of minimal submanifolds is a bounded embedding.
Findings
Ricci curvature conditions for minimal submanifolds
Bounded embedding properties of Gauss maps
Results applicable to Euclidean space and spheres
Abstract
We present conditions on the Ricci curvature for complete, oriented, minimal submanifolds of Euclidean space, as well as the standard unit sphere, when the Gauss maps are bounded embeddings.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds