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Real Hypersurfaces in the Complex Quadric with Lie Invariant Structure Jacobi Operator

  • Young Jin Suh (a1) and Gyu Jong Kim (a1)

Abstract

We introduce the notion of Lie invariant structure Jacobi operators for real hypersurfaces in the complex quadric $Q^{m}=SO_{m+2}/SO_{m}SO_{2}$ . The existence of invariant structure Jacobi operators implies that the unit normal vector field $N$ becomes $\mathfrak{A}$ -principal or $\mathfrak{A}$ -isotropic. Then, according to each case, we give a complete classification of real hypersurfaces in $Q^{m}=SO_{m+2}/SO_{m}SO_{2}$ with Lie invariant structure Jacobi operators.

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This work was supported by grant Proj. No. NRF-2018-R1D1A1B-05040381 and the second by grant Proj. No. NRF-2018-R1A6A3A-01011828 from National Research Foundation of Korea. Young Jin Suh is the corresponding author.

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Real Hypersurfaces in the Complex Quadric with Lie Invariant Structure Jacobi Operator

  • Young Jin Suh (a1) and Gyu Jong Kim (a1)

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