The ( 2 , 1 ) metric can be calculated in two parts . The first part is due to the ( 2 , ) monopole . This metric includes the effects of the ( , 1)-monopole on the ( 2 , ) -monopole but does not include the ( , 1)-monopole itself . The second part of the metric is due to the ( , 1)-monopole . This is described in Section 2 . First , the Nahm data are introduced along with the groups acting on them . Gauge - invariant coordinates on M ( 2,1 ) are then defined from the Nahm data and a set of one - forms defined from the exterior derivatives of these coordinates . Tangent vectors dual to these one - forms are calculated and the metric expressed in terms of the tangent vectors . The calculation of the explicit metric is presented in Section 3 . In Section 4.1 another way of calculating the metric is discussed in which the physical description given above is very apparent . In this Section , the hyperKähler quotient construction is used to construct the metric on M ( 2,1 ) from the direct product of the ( 2 , [ 1])-monopole and 1 - monopole metrics .