# Did Clifford introduce the “Clifford torus”, and for what purpose?

The Clifford torus shows up a lot in differential geometry in connection with minimal surfaces, for example in the Lawson's conjecture, the Oh's Conjecture, etc. It can be described as the following surface in $\mathbb C^2$: $$T = \left\{ (z_1, z_2) \in \mathbb C^2: |z_1| = |z_2| = \frac{1}{\sqrt 2}\right\}.$$

I'd like to know in what context it was introduced, and why it is called the Clifford torus. From the Wikipedia page, Clifford is a geometer, but it does not mention if he used this torus in any way.

The Clifford torus was introduced by Clifford in 1873, not as embedded into $\mathbb{R}^4$ or $\mathbb{C}^2$, but first projectively and then intrinsically, by identifying the opposite sides of a flat parallelogram, a commonplace method in modern topology textbooks. The embedding into $\mathbb{R}^4$ first appeared in Killing's Die Nichteuklidischen Raumformen in Analytischer Behandlung (Non-Euclidean Space Forms in Analytic Treatment, 1885), where he also pointed out that the embedded torus is contained in a $3$-sphere. The name "Clifford torus" was given by Klein in Zur Nicht-Euklidischen Geometrie (On Non-Euclidean Geometry, 1890), in this book he also used Clifford's identification method to construct the "Klein bottle".