Real Hypersurfaces in CP² and CH² Equipped With Structure Jacobi Operator Satisfying L_ξl =▽_ξl

Konstantina Panagiotidou, Philippos J. Xenos

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DOI: 10.4236/apm.2012.21001                

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.

Keywords

Real Hypersurfaces; Complex Projective Space; Complex Hyperbolic Space; Lie Derivative; Structure Jacobi Operator

Conflicts of Interest

The authors declare no conflicts of interest.

References

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