Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

Jeong, Imsoon ; Pérez, Juan de Dios ; Suh, Young Jin ; Woo, Changhwa

Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 543-552

Résumé

On a real hypersurface $M$ in a complex two-plane Grassmannian ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ we have the Lie derivation $\mathcal{L}$ and a differential operator of order one associated with the generalized Tanaka–Webster connection ${{\widehat{\mathcal{L}}}^{\left( k \right)}}$ . We give a classification of real hypersurfaces $M$ on ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ satisfying $\widehat{\mathcal{L}}_{\xi }^{\left( k \right)}\,S\,=\,{{\mathcal{L}}_{\xi }}S$ , where $\xi$ is the Reeb vector field on $M$ and $s$ the Ricci tensor of $M$ .

Détail

DOI : 10.4153/CMB-2017-049-5

Mots-clés : 53C40, 53C15, real hypersurface, complex two-plane Grassmannian, Hopf hypersurface, shape operator, Ricci tensor, Lie derivation