A Veronese surface is a smooth two-dimensional surface given by embedding the projective plane into projective 5-space by the homogeneous parametric equations
 |
The surface can be projected smoothly into four-space, but all three-dimensional projections have singularities (Coffman). The projections of these surfaces in three
dimensions are called Steiner surfaces. The volume of the Veronese surface is 
.
The Veronese projective plane is a spherical realization of the real projective construction as an embedded minimal
surface in unit 
.
With that spherical normalization, it has area 
and Morse index 5. Carlotto et al. (2026) characterized
it by index 5 among closed connected smooth embedded nongreat minimal
surfaces in unit 
.
Carlotto et al. (2026) report AI assistance with the mathematical proof.
