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Symplectic scalar curvature on the supermanifold of differential forms

Departamento de Matemáticas, Universidad de Sonora, Blvd. Encinas y Rosales, Col. Centro, Hermosillo, Sonora, C. P. 83000, México

E-mail Address: rosalia.hernandez@unison.mx

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J. A. Vallejo

Departamento de Matemáticas Fundamentales, Universidad Nacional de Educación a Distancia, C. Juan del Rosal 10, Madrid, CP 28040, Spain

E-mail Address: jvallejo@mat.uned.es

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Yury Vorobev

Departamento de Matemáticas, Universidad de Sonora, Blvd. Encinas y Rosales, Col. Centro, Hermosillo, Sonora, C. P. 83000, México

E-mail Address: yury.vorobev@unison.mx

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https://doi.org/10.1142/S0219887823501554Cited by:0 (Source: Crossref)

Abstract

In 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.

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