Real Hypersurfaces in CP2 and CH2 Equipped With Structure Jacobi Operator Satisfying Lξl =▽ξl

Konstantina  Panagiotidou; Philippos J.  Xenos

doi:10.4236/apm.2012.21001

Konstantina Panagiotidou, Philippos J. Xenos

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

Cite this paper: K. Panagiotidou and P. Xenos, "Real Hypersurfaces in CP² and CH² Equipped With Structure Jacobi Operator Satisfying L_ξl =▽_ξl," Advances in Pure Mathematics, Vol. 2 No. 1, 2012, pp. 1-5. doi: 10.4236/apm.2012.21001.

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