Transactions of the american mathematical society vol:348 issue:4 pages:1633-1646
In this paper, we study 3-dimensional totally real submanifolds of S-6(1). If this submanifold is contained in some 5-dimensional totally geodesic S-5(1), then we classify such submanifolds in terms of complex curves in CP2(4) lifted via the Hopf fibration S-5(1) --> CP2(4). We also show that such submanifolds always satisfy Chen's equality, i.e. delta(M) = 2, where delta(M)(p) = tau(p)-inf K(p) for every p is an element of M. Then we consider 3-dimensional totally real submanifolds which are linearly full in S-6(1) and which satisfy Chen's equality. We classify such submanifolds as tubes of radius pi/2 in the direction of the second normal space over an almost complex curve in S-6(1).