2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95851Basic properties of even (odd) supermanifolds endowed with a connection respecting a given symplectic structure are studied. Such supermanifolds can be considered as generalization of Fedosov manifolds to the supersymmetric case.10 pages, Latex, Contribution to Special Issue of Vestnik of Tomsk State Pedagogical University devoted to 70th Anniversary of Physical and Mathematical DepartmentHigh Energy Physics - Theorytext