Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms
Metadatos
Mostrar el registro completo del ítemEditorial
Gruyter Open
Materia
Real hypersurfaces Structure Jacobi operator Cho operator Non-flat complex space forms
Fecha
2015Referencia bibliográfica
Panagiotidou, K.; Pérez Jiménez, J.D. Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms. Open Mathematics, 13(1): 321-332 (2015). [http://hdl.handle.net/10481/38572]
Patrocinador
This paper is part of the work produced during the first author’s visit at the IEMath-Granada and supported by it. The second author is supported by grant Proj. No. NRF-2011-220-C0002 from National Research Foundation of Korea and by MCT-FEDER Grant MTM2010-18099.Resumen
In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results concerning real hypersurfaces in complex hyperbolic space satisfying the above conditions are also provided.