REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WHOSE SHAPE OPERATOR IS OF CODAZZI TYPE IN GENERALIZED TANAKA-WEBSTER CONNECTION

Abstract

In this paper, we give a non-existence theorem of Hopf hypersurfaces in complex two-plane Grassmannians <TEX>$G_2(\mathbb{C}^{m+2})$</TEX>, <TEX>$m{\geq}3$</TEX>, whose shape operator is of Codazzi type in generalized Tanaka-Webster connection <TEX>$\hat{\nabla}^{(k)}$</TEX>.