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http://dx.doi.org/10.4134/JKMS.j200311

A NEW CLASSIFICATION OF REAL HYPERSURFACES WITH REEB PARALLEL STRUCTURE JACOBI OPERATOR IN THE COMPLEX QUADRIC  

Lee, Hyunjin (Research Institute of Real and Complex Manifolds (RIRCM) Kyungpook National University)
Suh, Young Jin (Department of Mathematics & RIRCM Kyungpook National University)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 895-920 More about this Journal
Abstract
In this paper, first we introduce the full expression of the Riemannian curvature tensor of a real hypersurface M in the complex quadric Qm from the equation of Gauss and some important formulas for the structure Jacobi operator Rξ and its derivatives ∇Rξ under the Levi-Civita connection ∇ of M. Next we give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, ∇ξRξ = 0, in the complex quadric Qm 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 Qm, for m ≥ 3.
Keywords
Reeb parallel structure Jacobi operator; ${\mathcal{C}}$-parallel structure Jacobi operator; singular normal vector field; Kahler structure; complex conjugation; complex quadric;
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