Some Conditions Concerning the Shape Operator of a Real Hypersurface in Complex Projective Space Pérez Jiménez, Juan De Dios Pérez López, David kth Generalized Tanaka–Webster connection Complex projective space Real hypersurface Shape operator Lie derivative Funding for open access publishing: Universidad de Granada/CBUA Funding for open access charge: Universidad de Granada/CBUA. Let M be a real hypersurface of a complex projective space. For any operator B on M and any nonnull real number k, we can define two tensor fields of type (1,2) on M, BF(k) and BT(k) . We will classify real hypersurfaces in complex projective space for which BF(k) and BT(k) either take values in the maximal holomorphic distribution D or are parallel to the structure vector field ξ , in the particular case of B= A , where A denotes the shape operator of M. We also introduce the concept of AF(k) and AT(k) being D -recurrent and classify real hypersurfaces such that either AF(k) or AT(k) are D -recurrent. 2023-09-13T08:11:51Z 2023-09-13T08:11:51Z 2023-08-01 journal article Pérez, J.d.D., Pérez-López, D. Some Conditions Concerning the Shape Operator of a Real Hypersurface in Complex Projective Space. Bull. Iran. Math. Soc. 49, 55 (2023). [https://doi.org/10.1007/s41980-023-00797-1] https://hdl.handle.net/10481/84383 10.1007/s41980-023-00797-1 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature