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I mean that it doesn't require any assumptions as to a specific form of the torsion tensor, e.g. with vanishing traceless part. In other words, that the above mentioned decomposition of the torsion tensor doesn't imply any geometrical constraints on its components.

These are the references: Novello and Sabbata & Gasperini.

Is there anyone who can answer? Does the question need clarification?

When extending general relativity to include electromagnetism, several authors (e.g. Novello, Sabbata ecc.) assume that the traceless part of the torsion tensor vanishes or is deliberately set to zero. Then, either the trace or axial part of the torsion is used in association with the...