Atlas Paclet Symbol

Riemann - calculation of Riemannian tensor

Riemann[id]
allows one to calculate the curvature tensor.

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id - variable - corresponding identifier

The procedure is only available if the curvature 2-forms have been calculated (see Curvature).

Declare forms:

Declare vectors:

Declare constant :

Declare coframe:

Declare frame:

Declare metric on S³ (see Metric):

In[7]:=

Out[7]=

Connection calculation:

In[8]:=

Out[8]=

Curvature calculation:

In[9]:=

Out[9]=

Riemannian tensor calculation:

Declare forms:

Declare vectors:

Declare coframe:

Declare frame:

Connection definition:

Connection declaration:

In[10]:=

Out[10]=

Curvature calculation:

In[11]:=

Out[11]=

In[12]:=

Out[12]//MatrixForm=

In[13]:=

Out[13]=

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Riemann - calculation of Riemannian tensor

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