Geodesic
Real Hypersurfaces in the Complex Quadric with Lie Invariant Structure Jacobi Operator
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 204-221

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DOI

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.
DOI : 10.4153/S0008439519000080
Mots-clés : invariant structure Jacobi operator, A-isotropic, A-principal, Kähler structure, complex conjugation, complex quadric 
Suh, Young Jin; Kim, Gyu Jong. Real Hypersurfaces in the Complex Quadric with Lie Invariant Structure Jacobi Operator. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 204-221. doi: 10.4153/S0008439519000080
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     title = {Real {Hypersurfaces} in the {Complex} {Quadric} with {Lie} {Invariant} {Structure} {Jacobi} {Operator}},
     journal = {Canadian mathematical bulletin},
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     year = {2020},
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     doi = {10.4153/S0008439519000080},
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