cov - covariant derivative

cov[v, expr]
covv[expr]
allows one to calculate the covariant derivative on an expression along given vector field.
  • expr - any expression. v - vector field.
  • The derivative has the following properties.
  • - For any vector field X and 0-form f we have: X(f)=X(d(f))
  • - For vector fields X, Y and Z we have: X(Y+Z)=X(Y)+X(Z) and X+Y for any functions f and h.
  • - For any vector field X and tensor fields and T the Leibniz rule for the derivative takes place: X(T)=(X(T))+T(X())