On the Riemannian curvature tensor of a real hypersurface in a complex projective space

We consider real hypersurfaces M in complex projective space equipped with both the Levi–Civita and generalized Tanaka–Webster connections and classify them when the covariant derivatives associated with both connections, either in the direction of the structure vector field or any direction of the...

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Bibliographic Details
Published in:Mathematische Nachrichten 2016-12, Vol.289 (17-18), p.2263-2272
Main Author: Perez, Juan de Dios
Format: Article
Language:English
Subjects:
53B25
53C15
complex projective space
g-Tanaka-Webster connection
real hypersurface
Riemannian curvature tensor
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Summary:We consider real hypersurfaces M in complex projective space equipped with both the Levi–Civita and generalized Tanaka–Webster connections and classify them when the covariant derivatives associated with both connections, either in the direction of the structure vector field or any direction of the maximal holomorphic distribution, coincide when applying to the Riemannian curvature tensor of the real hypersurface.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201500318