Hernández-Amador, Rosalía G.Vallejo Rodríguez, José AntonioVorobiev, Yu2024-12-202024-12-202023-04-08Hernández-Amador, Rosalía G.; Vallejo Rodríguez, José Antonio; Vorobiev, Yu; Symplectic scalar curvature on supermanifolds, International Journal of Geometric Methods in Modern PhysicsVol. 20, No. 09, 2350155 (2023), https://doi.org/10.1142/S02198878235015541793-6977https://doi.org/10.1142/S0219887823501554https://hdl.handle.net/20.500.14468/25022This is a Submitted Manuscript of an article published by World Scientific in "International Journal of Geometric Methods in Modern Physics Vol. 20, No. 09, 2350155 (2023)", available at: https://doi.org/10.1142/S0219887823501554 Este es el manuscrito enviado del artículo publicado por World Scientific en "International Journal of Geometric Methods in Modern Physics Vol. 20, No. 09, 2350155 (2023)", disponible en línea: https://doi.org/10.1142/S0219887823501554In this paper, we study the notion of symplectic scalar curvature on the supermanifold over an ordinary Fedosov manifold whose structural sheaf is that of differential forms. In this purely geometric context, we introduce two families of odd super-Fedosov structures, the first one is very general and uses a graded symmetric connection, leading to a vanishing odd symplectic scalar curvature, while the second one is based on a graded non-symmetric connection and has a nontrivial odd symplectic scalar curvature. As a simple example of the second case, we determine that curvature when the base Fedosov manifold is the torus.eninfo:eu-repo/semantics/openAccess12 Matemáticas::1204 GeometríaartículoSymplectic curvaturesupermanifoldsFedosov structures