Reduction of principal superbundles, Higgs superfields, and supermetric
  By virtue of the well-known theorem, a structure Lie group G of a principal bundle P is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/H. In gauge theory, such sections are treated as classical Higgs fields, and are exemplified by Riemannian and pseudo-Riemannian metrics. This theorem is extended to a certain class of principal superbundles, including a graded frame superbundle with a structure general linear supergroup. Each reduction of this structure supergroup to an orthgonal-symplectic supersubgroup is associated to a supermetric on a base supermanifold. 
G. Sardanashvily