... Proceedings of the Meeting on Quaternionic Structures in Mathematics and Physics, Trieste, 1994; SISSA, Trieste, ILAS/FM-6, 1996, http://www.emis.de/proceedings/QSMP94/index.html [G-P-V] S.G. Gindikin, ... characteristic and quaternionic Kdhler manifolds, Preprint Erwin Schrodinger Institut 466 (1997) (32 pp.) [A-V-L] D.V. Alekseevsky, A.M. Vinogradov, V.V. Lychagin: Geometry I, EMS 28, Springer, Berlin, ... and Z on M of pure degree. Next we are going to define quaternionic supermanifolds and quaternionic Kahler supermanifolds. First we define the notion of almost quaternionic structure. Definition...