Vol. 40, No. 1, 1972

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Isometric immersions of space forms in space forms

John Douglas Moore

Vol. 40 (1972), No. 1, 157–166

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
Received: 30 October 1970
Published: 1 January 1972
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara CA 93106
United States