Submanifolds with constant Jordan angles
J. Jost, Y. L. Xin, Ling Yang
TL;DR
This paper introduces the concept of submanifolds with constant Jordan angles to analyze minimal submanifolds in higher codimension, providing a new geometric perspective on Lawson-Osserman's counterexample to the Bernstein problem.
Contribution
It defines and explores submanifolds with constant Jordan angles, linking this concept to the characterization of Lawson-Osserman's cone in minimal submanifold theory.
Findings
Characterization of Lawson-Osserman's cone via Jordan angles
Introduction of the CJA concept for submanifolds
Analysis of the second fundamental form in this context
Abstract
To study the Lawson-Osserman's counterexample to the Bernstein problem for minimal submanifolds of higher codimension, a new geometric concept, submanifolds in Euclidean space with constant Jordan angles(CJA), is introduced. By exploring the second fundamental form of submanifolds with CJA, we can characterize the Lawson-Osserman's cone from the viewpoint of Jordan angles.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Point processes and geometric inequalities