xTras SymbolSee Also »|More About »

SymRiemann

SymRiemann
is a reserved word in xTras. It is used to generate the name of the symmetrized Riemann curvature tensor associated to a connection acting on a tangent bundle.
  • The symmetrized Riemann tensor is only defined when there is a metric and no torsion.
  • The symmetrized Riemann tensor is given by .
  • The Riemann tensor in terms of the symmetrized Riemann tensor reads .
  • The symmetrized Riemann tensor has the following symmetries: P_(abcd)=P_((ab)(cd)), P_(abcd)=R_(cdab), P_((abc)d)=0.