Ricci-corrected derivatives and invariant differential operators (Q2567136)

The study of differential invariants is important both for the algebraic approach to differential equations as well as for differential geometry. This paper deals with the construction of invariant differential operators for structures known as parabolic geometries. The notion of Ricci-corrected differentiation is introduced which enables the authors to simplify the explicit formulas for standard linear invariant differential operators given in the paper [\textit{A. Čap, J. Slovák} and \textit{V. Souček}, Differ. Geom. Appl. 12, No. 1, 51--84 (2002; Zbl 0969.53004)]. Moreover, they extend the formulas to arbitrary parabolic structures. Also, the Weyl jet operator and its components, the Ricci-corrected Weyl derivatives, are uncovered. The paper is well-written with two appendices and adequate referencing.