Isometric immersions of space forms in space forms

John Douglas Moore

Vol. 40 (1972), No. 1, 157–166

DOI: 10.2140/pjm.1972.40.157

Abstract

Let M be a connected n-dimensional space form isometrically immersed in a simply connected (2n − 1)-dimensional space form of strictly larger curvature. If M is minimal, it is proven that it must be a piece of the flat Clifford torus in the (2n − 1)-sphere. If M is complete and simply connected, it is proven that M possesses a global coordinate system whose coordinate vectors are unit-length asymptotic vectors.

Mathematical Subject Classification 2000

Primary: 53C40

Milestones

Received: 30 October 1970

Published: 1 January 1972