A duality for hyperconvex curves (Q2571707)

As is well known, a hypercomplex curve is a curve \(\xi^1\) in \(\mathbb{P}(\mathbb{R}^n)\) such that any \(n\) distinct points of the curve are in direct sum. In the present paper the author gives a property of duality of those curves when they admit, furthermore, an osculating flag. Namely, if \((\xi^1,\dots, \xi^{n-1})\) is a continuous curve of osculating flags of a hyperconvex curve \(\xi^1\), then the author proves that the curve \(\xi^{n-1}\) is hyperconvex, too, and admits a curve of osculating flags.