Abstract
Recently in [1], Perez and Santos classified real hypersurfaces in complex projective space CPn for n ≥ 3, whose Lie derivative of structure Jacobi operator in the direction of the structure vector field coincides with the covariant derivative of it in the same direction. The present paper completes the investigation of this problem studying the case n = 2 in both complex projective and hyperbolic spaces.
Highlights
A complex n-dimensional Kaehler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by Mn c
In [1], Perez and Santos classified real hypersurfaces in complex projective space Pn for n 3, whose Lie derivative of structure Jacobi operator in the direction of the structure vector field coincides with the covariant derivative of it in the same direction
The present paper completes the investigation of this problem studying the case n = 2 in both complex projective and hyperbolic spaces
Summary
A complex n-dimensional Kaehler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by Mn c. The Lie derivative of the structure Jacobi operator with respect to was investigated by Perez, Santos, Suh (see [7]). They classified real hypersurfaces in Pn ( n 3 ), whose structure Jacobi operator satisfies the condition: L l = 0. The parallelness of structure Jacobi operator in combination with other conditions was another problem that was studied by many others such as Ki, Kim, Perez, Santos, Suh (see [11,12]). Perez-Santos (see [1]) studied real hypersurfaces in Pn for n 3 , whose structure Jacobi operator satisfies the relation:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
