TOTALLY REAL SURFACES IN $S^6$

Abstract

\n \n \nThe normal bundle $\\bar \\nu$ of a totally real surface $M$ in $S^6$ splits as $\\bar\\nu= JTM\\oplus \\bar\\mu$ where $TM$ is the tangent bundle of $M$ and\xa0 $\\bar\\mu$ is sub\xadbundle of $\\bar\\nu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) \\in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic). \n \n \n