\(k\)-Dirac operator and the Cartan-Kähler theorem. (English) Zbl 1313.58001

Salač, Tomáš

Arch. Math., Brno 49, No. 5, 333-346 (2013).

Summary: We apply the Cartan-Kähler theorem for the \(k\)-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for \(k=2\) the tableaux of the first prolongations of these two operators are involutive. This gives us a new characterization of the set of initial conditions for the 2-Dirac operator.

MSC:

58A17	Pfaffian systems
53C27	Spin and Spin\({}^c\) geometry
58A15	Exterior differential systems (Cartan theory)

Keywords:

Clifford analysis; parabolic Dirac operator; Cartan-Kähler theorem