Μελέτη πραγματικών υπερεπιφανειών μη ευκλείδειων μιγαδικών χώρων μορφής

Abstract

J. de Dios Perez, F. G. Santos and Y. J. Suh in [29], studied real hypersurfaces of dimension greater than 3 in complex projective spaces, whose Jacobi structure operator is of Codazzi type. In chapter 2 we study real hypersurfaces under the same condition, fulfilling the case of hyperbolic spaces of dimension n > 3 as long as the case of 3dimensional hypersurfaces. M. Ortega, J. de Dios Perez and F. G. Santos in [24] studied real hypersurfaces of dimension greater than 3, in complex space forms, whose Jacobi structure operator is parallel. J. de Dios Perez and F. G.Santos in [27] studied real hypersurfaces of dimension greater than 3 with recurrent structure Jacobi operator. In chapter 3 we improve [27] in dimension 3, by studying real hypersurfaces with D recurrent structure Jacobi operator, in complex planes. Furthermore we improve [24] by studying real hypersurfaces of dimension n > 3 with recurrent structure Jacobi operator. J. T. Cho and U H. Ki in [13] classified real hypersurfaces of dimension greater than 3, in complex projective spaces, which satisfy the conditions l = l and lA = Al everywhere in the real hypersurface M. In chapter 4 we improve the previous paper by classifying real hypersurfaces in complex space forms of dimension 2n (n 2) satisfying the condition l = l in D and the condition lA = Al either in D or in D?. Moreover we classify real hypersurfaces in complex space forms of dimension 2n (n 2) satisfying the condition l = l in D and the condition (r l) = , 2 C1 either in D or in D?.