ManifoldGeometry.project_oblique
================================

.. py:method:: t3toolbox.manifold.ManifoldGeometry.project_oblique(v)

   .. code-block:: python

      def project_oblique(
              self,
              v:  T3Tangent,
      ) -> T3Tangent:  # gauged tangent at v's frame (the SAME vector)


   Gauge ``v``'s variations while preserving the represented tangent vector (oblique projection).

   Returns a tangent at the same frame representing the SAME vector as ``v`` but gauged, so that on
   an orthogonal minimal-rank frame :py:meth:`inner` / :py:meth:`norm` give the true Hilbert-Schmidt
   values.

   **Safe mode** requires ``v``'s frame to be **orthogonal** (raises otherwise); skipped under
   ``safety.unsafe()`` / a jax trace.