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Real hypersurfaces in a complex projective space with pseudo- 𝔻 -parallel structure Jacobi operator

Hyunjin Lee, Juan de Dios Pérez, Young Jin Suh (2010)

Czechoslovak Mathematical Journal

We introduce the new notion of pseudo- 𝔻 -parallel real hypersurfaces in a complex projective space as real hypersurfaces satisfying a condition about the covariant derivative of the structure Jacobi operator in any direction of the maximal holomorphic distribution. This condition generalizes parallelness of the structure Jacobi operator. We classify this type of real hypersurfaces.

Ricci curvature of real hypersurfaces in complex hyperbolic space

Bang-Yen Chen (2002)

Archivum Mathematicum

First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.

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