GEOMETRICAL AND TOPOLOGICAL OBSTRUCTIONS OF MINIMAL HYPERSURFACES IN S~5(1)

<正> In this report, we obtain a topological obstruction for a 4-dimensional manifold to be a minimal hypersurface in S~5(1), i. e. if M~4→S~5(1) is minimal, then its signature is zero and |w~|=|W~-| holds everywhere, here W~+ and W~- are the self-dual and anti-self-dual parts of the Weyl tensor of M, respectively. We also