TL;DR
This paper introduces the $W_2$-curvature tensor for super Riemannian manifolds, computes it for super twisted products, and explores conditions for flatness and Ricci-flatness, revealing structural characterizations.
Contribution
It defines the $W_2$-curvature tensor on super Riemannian manifolds and analyzes its properties on super twisted product spaces, including flatness and Ricci-flatness conditions.
Findings
Computed the $W_2$-curvature tensor on super twisted product spaces.
Characterized $W_2$-curvature flat super twisted product manifolds.
Showed that Ricci-flat super twisted products can be expressed as super warped products.
Abstract
In this paper, we define the -curvature tensor on super Riemannian manifolds. And we compute the curvature tensor, the Ricci tensor and the -curvature tensor on super twisted product spaces. Furthermore, we investigate the -curvature flat super twisted product manifolds. And, we get a result that a mixed Ricci-flat super twisted product semi-Riemannian manifold can be expressed as a super warped product semi-Riemannian manifold.
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