Normal scalar curvature conjecture and its applications
Zhiqin Lu
TL;DR
This paper proves the Normal Scalar Curvature Conjecture and the Bottcher-Wenzel Conjecture, and introduces new pinching theorems for minimal submanifolds in spheres, advancing understanding in differential geometry.
Contribution
It provides the first proofs of two major conjectures and develops new geometric pinching theorems for minimal submanifolds.
Findings
Proof of the Normal Scalar Curvature Conjecture
Proof of the Bottcher-Wenzel Conjecture
New pinching theorems for minimal submanifolds in spheres
Abstract
In this paper, we proved the Normal Scalar Curvature Conjecture and the Bottcher-Wenzel Conjecture. We also established some new pinching theorems for minimal submanifolds in spheres.
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