Normal scalar curvature conjecture and its applications
arXiv:0803.0502 · doi:10.1016/j.jfa.2011.05.002
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.
minor and final typo corrections
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Cited by in corpus (26)
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- On Chern's conjecture for minimal hypersurfaces in spheres
- New Developments in Mean Curvature Flow of Arbitrary Codimension Inspired By Yau Rigidity Theory
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- One parameter generalization of BW inequality and its application to open quantum dynamics
- On some conjectures by Lu and Wenzel
- Rigidity of closed CSL submanifolds in the unit sphere
- Normal scalar curvature inequality on the focal submanifolds of isoparametric hypersurfaces
- Classification of Moebius homogeneous Wintgen ideal submanifolds
- On Yau rigidity theorem for minimal submanifolds in spheres
- Surfaces pinched by normal curvature for mean curvature flow in space forms
- Sectional nonassociativity of metrized algebras
- New result on Chern conjecture for minimal hypersurfaces and its application
- Wintgen ideal submanifolds of codimension two, complex curves, and Moebius geometry
- Sum of squares representation for the Böttcher-Wenzel biquadratic form
- Variational formulas of higher order mean curvatures
- Some generalizations of the DDVV and BW inequalities
- Pinching rigidity of minimal surfaces in spheres
- Remarks on the Bottcher-Wenzel Inequality
- Minimal surfaces in a unit sphere pinched by intrinsic curvature and normal curvature
- Constraints for the spectra of generators of quantum dynamical semigroups
- Geometric inequalities for Einstein totally real submanifolds in a complex space form
- DDVV-type inequality for Hermitian matrices