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2 results

Real Hypersurfaces in Complex Two-Plane Grassmannians with GTW Harmonic Curvature
Juan de Dios Pérez, Young Jin Suh, Changhwa Woo
Journal:

Canadian Mathematical Bulletin / Volume 58 / Issue 4 / 01 December 2015

Published online by Cambridge University Press:

20 November 2018, pp. 835-845

Print publication:

01 December 2015
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We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians with harmonic curvature with respect to the generalized Tanaka–Webster connection if they satisfy some further conditions.

Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator
Imsoon Jeong, Seonhui Kim, Young Jin Suh
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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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 ${{\nabla }_{\xi }}{{R}_{\xi }}\,=\,0$.