Vol. 78, No. 1, 1978

Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Focal sets of submanifolds

Thomas E. Cecil and Patrick J. Ryan

Vol. 78 (1978), No. 1, 27–39

This is a study of the manifold structure of the focal set of an immersed submanifold in a real space form M. A typical result is the following:

Theorem. Let M be an orientable (immersed) hypersurface in M which is complete with respect to the induced metric. Let λ be a differentiable principal curvature of constant multiplicity ν > 1 on M. Then the focal map fλ factors through an immersion of the (n ν)-dimensional manifold Mλ into M. In this way, fλ(M) is an immersed submanifold of M.

Mathematical Subject Classification 2000
Primary: 53C40
Received: 2 May 1977
Revised: 15 February 1978
Published: 1 September 1978
Thomas E. Cecil
Department of Mathematics
College of the Holy Cross
Worcester MA 01610-2395
United States
Patrick J. Ryan