Real Hypersurfaces with Invariant Normal Jacobi Operator in the Complex Hyperbolic Quadric
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초록
We introduce the notion of Lie invariant normal Jacobi operators for real hypersurfaces in the complex hyperbolic quadric Qm∗ = SOom,2/SOmSO2. The invariant normal Jacobi operator implies that the unit normal vector field N becomes $\frak A$-principal or A-isotropic. Then in each case, we give a complete classification of real hypersurfaces in Qm∗= SOom,2/SOmSO2 with Lie invariant normal Jacobi operators.
Abstract
We introduce the notion of Lie invariant normal Jacobi operators for real hypersurfaces in the complex hyperbolic quadric Qm∗ = SOom,2/SOmSO2. The invariant normal Jacobi operator implies that the unit normal vector field N becomes $\frak A$-principal or A-isotropic. Then in each case, we give a complete classification of real hypersurfaces in Qm∗= SOom,2/SOmSO2 with Lie invariant normal Jacobi operators.
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