An intrinsic characterization of a class of minimal surfaces in constant curvature manifolds

G. D. Johnson

Vol. 149 (1991), No. 1, 113–125

DOI: 10.2140/pjm.1991.149.113

Abstract

Let X be an N-manifold of constant sectional curvature. A class of minimal surfaces in X, called exceptional minimal surfaces, will be defined in terms of the structure of their normal bundles. It will be shown that these surfaces can be characterized intrinsically in a way that generalizes the Ricci condition for minimal surfaces in Euclidean 3-space. It will also be shown that these surfaces are rigid when N is even and belong to 1-parameter families of isometric surfaces when N is odd.

Mathematical Subject Classification 2000

Primary: 53C42

Secondary: 49Q05, 58E20

Milestones

Received: 18 October 1989

Published: 1 May 1991