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A complex ^-dimensional Kahler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by Mn(c). A complete and simply connected complex space form consists of a complex projective space PnC, a complex Euclidean space Cn or a complex hyperbolic space HnC, according as c > 0, c = 0 or c < 0. In this paper, we consider a real hypersurface M in Mn{c). Typical examples of M in PnC are the six model spaces of type A\,A2,B,C,D and E (cf.[10]),and the ones of M in HnC are the four model spaces of type Aq,A\,A2 and B (cf.[1]), which are all given as orbits under certain Lie subgroups of the group consisting of allisometries of PnC or HnC. Denote by (<f>,,r},g) the almost contact metric structure of M induced from the almost complex structure of Mn{c) and A the shape operator of M. Eigenvalues and einvectors of A are called principal curvatures and principal vectors, respectively. Many differentialgeometers have studied M from various points of view. In particular, Berndt [1] and Takagi [10] investigated the homogeneity of M. According to Takagi's classificationtheorem and Bemdt's one, the principal curvatures and their multiplicitiesof homogeneous real hypersurfaces in Mn(c) are given. Moreover, it is very interesting to characterize homogeneous real hypersurfaces of Mn{c). There are many characterizations of homogeneous ones of type A since these examples have a lot of beautiful geometric properties, where type A means type A\ or A2 in PnC and type Ao,A\ or A2 in HnC. Okumura [8] and Montiel-Romero [7] proved the fact in PnC and HnC, respectively that M

Certain characterizations of real hypersurfaces of type $A$ in a complex space form