Willmore submanifolds in the unit sphere via isoparametric functions
Yuquan Xie
TL;DR
This paper proves that focal submanifolds of isoparametric hypersurfaces with six principal curvatures in the sphere are Willmore, extending previous work on the geometric properties of these submanifolds.
Contribution
It establishes that all focal submanifolds of isoparametric hypersurfaces with six principal curvatures are Willmore, providing new insights into their geometric structure.
Findings
Focal submanifolds with six principal curvatures are Willmore.
Extension of previous results on isoparametric hypersurfaces.
Advancement in understanding submanifold geometry in spheres.
Abstract
This paper is a continuation of [TY12] and [QTY13]. We show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Numerical Analysis Techniques