  We determine normal forms and ranks of tensors of border rank at most three.
We present a differential-geometric analysis of limits of secant planes in a
more general context. In particular there are at most four types of points on
limiting trisecant planes for cominuscule varieties such as Grassmannians. We
also show the singular locus of the first two secant varieties of all triple
Segre products has codimension at least two.
