A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms
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The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F X ( k ) is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by F X and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that F X S = S F X , where S denotes the Ricci tensor of M and a further condition is satisfied, are classified.
1997 ◽
Vol 40
(3)
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pp. 257-265
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2010 ◽
Vol 33
(1)
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pp. 123-134
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2017 ◽
Vol 21
(2)
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pp. 305-318
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