Abstract:
Chen-Ogiue [1] showed that if M is an n-dimensional compact totally real minimal submanifold immersed inMn (c) then M is totally geodesic 'fS n(n +1) 1 < c. 4(2n -1) The purpose of this manuscript is to study the geometry of an n- dimensional totally real maximal spacelike submanifold M immersed in an indefinite complex space form M(c),c 1:- O. We have generalized Chen- Ogiue's result by showing that if M is an n-dimensional compact totally real maximal spacelike submanifold of M;+P(c),C1:-0, thenS~(n+1)(n+2p)c. 4(2n+4p-l) Moreover, if S is less than (n +1)(n+2p) c then M is totally geodesic.
