This paper presents a series of constructions providing eleven-dimensional bosonic supergravity backgrounds. In particular, we treat Lorentzian manifolds given in terms of twisted products of six-dimensional Lorentzian manifolds and five-dimensional Riemannian manifolds. By considering a representative flux 4-form adapted to this setting, we analyse the system of bosonic supergravity equations and describe the corresponding geometric constraints. The new supergravity backgrounds appear for special cases associated to the adapted flux 4-form. For example, we provide a relation of eleven-dimensional supergravity with Ricci-isotropic Walker manifolds, and illustrate several results in their terms and in terms of Ricci-flat Riemannian manifolds.

中文翻译：

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可分解 (6, 5) - 十一维超引力中的解

本文介绍了一系列提供 11 维玻色子超重力背景的结构。特别地，我们处理根据六维洛伦兹流形和五维黎曼流形的扭曲积给出的洛伦兹流形。通过考虑适合这种设置的代表性通量 4-形式，我们分析了玻色超重力方程组并描述了相应的几何约束。新的超重力背景出现在与适应的通量 4-形式相关的特殊情况下。例如，我们提供了 11 维超重力与 Ricci-isotropic Walker 流形的关系，并用它们的术语和 Ricci-flat Riemannian 流形说明了几个结果。