Submanifolds with constant Jordan angles

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.