We present new high angular resolution observations at near-IR wavelengths of the core of the Luminous Blue Variable \eta Carinae , using NAOS-CONICA at the VLT and VINCI at the VLT Interferometer ( VLTI ) .
The latter observations provide spatial information on a scale of 5 milli-arcsec or \sim 11 AU at the distance of \eta Carinae .
The present-day stellar wind of \eta Carinae is resolved on a scale of several stellar radii .
Assuming spherical symmetry , we find a mass loss rate of 1.6 \times 10 ^ { -3 } M _ { \odot } /yr and a wind clumping factor of 0.26 .
The VLTI data taken at a baseline of 24 meter show that the object is elongated with a de-projected axis ratio of approximately 1.5 ; the major axis is aligned with that of the large bi-polar nebula that was ejected in the 19th century .
The most likely explanation for this observation is a counter-intuitive model in which stellar rotation near the critical velocity causes enhanced mass loss along the rotation axis .
This results from the large temperature difference between pole and equator in rapidly rotating stars . \eta Carinae must rotate in excess of 90 per cent of its critical velocity to account for the observed shape .
The large outburst may have been shaped in a similar way .
Our observations provide strong support for the existence of a theoretically predicted rotational instability , known as the \Omega 
limit .