g["Liesphere"] =  Metric[
  SubMinus[i], SubMinus[j], SubMinus[k], SubMinus[l], SubMinus[m],
  SubMinus[n],
  -([DifferentialD]x1)^2 + ([DifferentialD]x2)^2 +
([DifferentialD]x3)^2 + ([DifferentialD]x4)^2 +
([DifferentialD]x5)*([DifferentialD]x6) + ([DifferentialD]x6)*(
[DifferentialD]x5),
  CoordinateSystem -> {x1, x2, x3, x4, x5, x6},
  TensorName -> h,
  StartIndex -> 1
  ]

Metric[SubMinus[i], SubMinus[j], SubMinus[k], SubMinus[l],
SubMinus[m], SubMinus[n], -([DifferentialD]x1)^2 +
([DifferentialD]x2)^2 + ([DifferentialD]x3)^2 +
([DifferentialD]x4)^2 + 2 [DifferentialD]x5 [DifferentialD]x6,
 CoordinateSystem -> {x1, x2, x3, x4, x5, x6}, TensorName -> h,
 StartIndex -> 1]