SUBMANIFOLDS WITH CONSTANT JORDAN ANGLES AND RIGIDITY OF THE LAWSON-OSSERMAN CONE

摘要

The Lawson-Osserman cone [24] is a four dimensional coassociative submanifold in R-7 in terms of Harvey-Lawson calibrated geometries [16] and the basic counterexample for Bernstein type results for minimal graphs of higher codimension in Euclidean space. We shall explore the geometry of this cone in terms of its basic property of constant Jordan angles and show a rigidity result within the class of coassociative submanifolds with constant Jordan angles. This will also shed new light on the higher codimension Bernstein problem.