PARAMETER SPACE FOR EIGENMAPS OF FLAT 3-TORI INTO SPHERES

The purpose of this paper is to parameterize range-equivalence classes of all eigenmaps of flat 3-tori $T^{3}$= $R^{3}$.LAMBDA., .LAMBDA.= $c_{1}$ $e_{1}$ + $c_{2}$ $e_{2}$ + $c_{3}$ $e_{3}$, into the standard unit spheres. In this paper, we classify $A_{ 0 \lambda}$( $T^{3}$)(cf..cint.1) which is contained in $A_{\lambda}$( $T^{3}$), are belonging to $A_{ 0 \lambda}$( $T^{3}$). Moreover, as an application, we show that the only minimally imbedded flat torus into ( $S^{5}$ , can) which is contained in $A_{ 0 \lambda}$( $T^{3}$) is the generalized Clifford torus.rd torus.