• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.895-920
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• 2021

In this paper, first we introduce the full expression of the Riemannian curvature tensor of a real hypersurface M in the complex quadric Q^m from the equation of Gauss and some important formulas for the structure Jacobi operator R_ξ and its derivatives ∇R_ξ under the Levi-Civita connection ∇ of M. Next we give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, ∇_ξR_ξ = 0, in the complex quadric Q^m for m ≥ 3. In addition, we also consider a new notion of 𝒞-parallel structure Jacobi operator of M and give a nonexistence theorem for Hopf real hypersurfaces with 𝒞-parallel structure Jacobi operator in Q^m, for m ≥ 3.