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arXiv · 2608.08781

Sasaki with torsion manifolds and string backgrounds

Beatrice Brienza·Anna Fino·Udhav Fowdar·Gueo Grantcharov
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Abstract

Motivated by the analogy with the Bismut connection in Hermitian geometry, we study Sasaki with torsion manifolds. In particular, we characterize co-Kähler-like and flat Sasaki with torsion manifolds, and we introduce the notion of a $\nabla$-Einstein manifold as the odd-dimensional analogue of the Bismut Hermite-Einstein condition. We provide non-compact examples and we study compact $\nabla$-Einstein manifold in dimension $5$ and $7$. We also develop a general framework for geometric flows of almost contact metric structures. In particular, we derive a flow for Sasaki with torsion structures that preserves the strong condition, that is, the closure of the torsion. Furthermore we prove that such flow is gauge-equivalent to the generalized Ricci flow and it is gauge-equivalent to the pluriclosed flow, after performing a trivial product with $S^1$.

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Beatrice Brienza, Anna Fino, Udhav Fowdar, Gueo Grantcharov. 2026-08-18. Sasaki with torsion manifolds and string backgrounds. https://arxiv.org/abs/2608.08781

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