New characterizations of ruled real hypersurfaces in complex projective space

Abstract: We consider real hypersurfaces

M

in complex projective space equipped with both the Levi-Civita and generalized Tanaka-Webster connections. For any nonnull constant

k

and any symmetric tensor field of type (1,1)

L

on

M

we can define two tensor fields of type (1,2) on

M

,

L_{F}^{(k)}

and

L_{T}^{(k)}

, related to both connections. We study the behaviour of the structure operator

p h i

with respect to such tensor fields in the particular case of

L = A

, the shape operator of

M

, and obtain some new characterizations of ruled real hypersurfaces in complex projective space.

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