Purity and hybridness of two tensors on a real hypersurface in complex projective space

Abstract

On a real hypersurface MM in complex projective space, we can define two tensor fields of type (1, 2), AF(k){A}_{F}^{\left(k)} and AT(k){A}_{T}^{\left(k)}, associated with the shape operator AA of the real hypersurface, for any nonnull real number kk. Following Tachibana [Analytic tensor and its generalization, Tohoku Math. J. 12 (1960), 208–221], we study the purity and hybridness of such tensors with respect to AA.

Keywords

• g-tanaka-webster connection
• complex projective space
• real hypersurface
• kth cho operator
• torsion operator
• pure tensor field
• hybrid tensor field
• 53c15
• 53b25