atlas[Torsion] - calculation of torsion 2-forms

Calling Sequence:

     Torsion(Id)

Parameters:

      Id - variable - torsion identifier

Description:

• The Torsion procedure calculates torsion 2-forms. If a connection is calculated or defined then torsion can be calculated completely otherwise just torsion identifier is declared as torsion. To get the result of the calculation use eval  or atlas[iota]  operators.
• The definition is as follows:  , where  are coframe 1-forms,    are connection 1-forms,  is the dimension.

Examples:

Example 1
restart:
with(atlas):

Declare forms:
Forms(e[j]=1,xi=1);

Declare vectors:
Vectors(X,Y,Z,E[j]);

Declare coframe:
Coframe(e[1]=x*d(x)+y*d(y),e[2]=x*d(y)-y*d(x));

Declare frame:
Frame(E[i]);

Connection definition:
omega[1,1]:=x*e[1];

omega[2,2]:=y*e[2];

omega[1,2]:=y*e[1];

omega[2,1]:=-x*e[2];

Connection declaration:
Connection(omega);

Torsion calculation:
Torsion(Omega);

eval(Omega);

'L[E[1]](E[2])'=L[E[1]](E[2]);

See Also:

atlas , atlas[Frame] , atlas[Coframe] , atlas[Metric] .