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Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 4 / 01 December 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 821-833
- Print publication:
- 01 December 2014
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- Article
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In this paper we give a characterization of a real hypersurface of Type
$\left( A \right)$ in complex two-plane Grassmannians 
${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$, which means a tube over a totally geodesic 
${{G}_{2}}\left( {{\mathbb{C}}^{m+1}} \right)$ in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$, by means of the Reeb parallel structure Jacobi operator 
${{\nabla }_{\xi }}{{R}_{\xi }}\,=\,0$.
