Bulletin of the Australian Mathematical Society

Research Article

Spherical submanifolds with special quadric representations

Jitan Lua1

a1 Division of Mathematics National Institute of Education Nanyang Technological University Singapore 259756 e-mail: NF2363833U@AC AD21.NTU.EDU.SG

Abstract

In this paper, we study submanifolds in the unit hypersphere satisfying S0004972700031671_inline1aS0004972700031671_inline1b where S0004972700031671_inline2 is the quadric representation of the submanifold, and B and C are two constant matrices. We prove that the totally geodesic submanifolds are the only submanifolds in the unit hypersphere whose quadric representations satisfy S0004972700031671_inline3

(Received August 07 1997)