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Real Hypersurfaces in the Complex Quadric with Lie Invariant Structure Jacobi Operator
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 1 / March 2020
- Published online by Cambridge University Press:
- 10 June 2019, pp. 204-221
- Print publication:
- March 2020
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- Article
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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.
