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arXiv · 1907.04661

Real hypersurfaces in the complex quadric with Reeb parallel structure Jacobi operator

Hyunjin Lee·Young Jin Suh
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Abstract

In this paper, we first introduce the full express of the Riemannian curvature tensor of a real hypersurface $M$ in complex quadric $Q^{m}$ from the equation of Gauss. Next we derive a formula for the structure Jacobi operator $R_{\xi}$ and its derivative under the Levi-Civita connection of $M$. We give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, $\nabla_{\xi}R_{\xi} =0$, in the complex quadric $Q^{m}$, $m \geq 3$.

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Hyunjin Lee, Young Jin Suh. 2019-07-09. Real hypersurfaces in the complex quadric with Reeb parallel structure Jacobi operator. https://arxiv.org/abs/1907.04661

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