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Physically relevant gauge and gravitational theories can be seen as specialmembers of hierarchies of more elaborate systems. The Yang-Mills (YM) system isthe first member of a hierarchy of Lagrangians which we will index by $p_1$,and the Einstein-Hilbert (EH) system of general relativity is the first memberof another hierarchy which we index by $p_2$. In this paper, we study theclassical equations of the $p_1 = 1,2$ YM hierarchy considered in thebackground of special geometries (Schwarzschild, deSitter,anti-deSitter) of the$p_2=1,2,3$ EH hierarchy. Solutions are obtained in various dimensions and leadto several examples of non-self-dual YM fields. When $p_1=p_2$ self-dualsolutions exist in addition. Their action is equal to the Chern-Pontryagincharge and can be compared with that of the non-self-dual solutions.Comment: LaTeX, 25 pages, 2 figures, new title, minor change

Finite energy–action solutions of p1 Yang–Mills equations on p2 Schwarzschild and deSitter backgrounds in dimensions d⩾4