Lie Derivatives of the Shape Operator of a Real Hypersurface in a Complex Projective Space
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kth g-Tanaka–Webster connectionComplex projective spaceReal hypersurfaceShape operatorLie derivatives
Pérez, J.d.D., Pérez-López, D. Lie Derivatives of the Shape Operator of a Real Hypersurface in a Complex Projective Space. Mediterr. J. Math. 18, 207 (2021). [https://doi.org/10.1007/s00009-021-01832-3]
SponsorshipMINECO-FEDER Project MTM 2016-78807-C2-1-P
We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. Associated with the generalized Tanaka–Webster connection we can define a differential operator of first order. For any nonnull real number k and any symmetric tensor field of type (1,1) B on M, we can define a tensor field of type (1,2) on M, B(k) T , related to Lie derivative and such a differential operator. We study symmetry and skew symmetry of the tensor A(k) T associated with the shape operator A of M.