About the geometry of almost para-quaternionic manifolds (Q734716)

The paper under review studies the integrability of an almost para-quaternionic structure on an almost para-quaternionic \(4n\)-dimensional manifold \((M,{\mathcal P})\) \((4n\geq 8)\), by applying similar considerations as \textit{D. V. Alekseevsky}, \textit{S. Marchiafava} and \textit{M. Pontecorvo} [Trans. Am. Math. Soc. 351, No. 3, 997--1014 (1999; Zbl 0933.53017)] by the so-called Oproiu connections, in case of almost quaternionic manifold. More precisely, using minimal para-quaternionic connections, the author defines canonical almost complex structure (respectively almost para-complex structure) on the twistor space (respectively on the reflector space) of \((M,{\mathcal P})\) and proves that \((M,{\mathcal P})\) is integrable iff there exists (infinitely many) locally defined, compatible compex and para-compex structures.