Real hypersurfaces in complex space forms concerned with the local symmetry

This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse image by the Hopf fibration of a real hypersurface M in complex space form M _m(4ε). In the second, we give a complete classification of real hypersurfaces in M _m(4ε) which satisfy the above geometric facts. The second author was supported by DGICYT research project BFM 2001-2871-C04-01 and the first and the third authors were supported by grant Proj. No. R14-2002-003-01001-0 from Korea Research Foundation, Korea 2006.