Real hypersurfaces with Reeb Jacobi operator of Codazzi type in the complex hyperbolic two-plane Grassmannians
DOI:
https://doi.org/10.7146/math.scand.a-150634Abstract
Utilizing the concept of Reeb Jacobi operator of Codazzi type, we investigate Hopf real hypersurfaces in the complex hyperbolic two-plane Grassmannian G∗2(Cm+2) which admit a constant Reeb function α along the Reeb direction of ξ. If the Reeb function α is constant along the Reeb direction, then the Reeb vector field ξ=−JN either belongs to the distribution D or the distribution D⊥. By virtue of this fact, we have proved a new result about Reeb Jacobi operator of Codazzi type according to the Reeb vector field ξ∈D⊥ or ξ∈D, respectively.
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