Geometric aspects of transversal Killing spinors on Riemannian flows

TL;DR

This paper investigates a special type of Killing spinor equation on Riemannian flows, establishing integrability conditions and classifying flows with solutions in specific geometric settings such as products, Sasakian manifolds, and 3D cases.

Contribution

It provides new integrability conditions and a partial classification of Riemannian flows admitting solutions to a Killing spinor type equation in certain geometric contexts.

Findings

Derived integrability conditions for the Killing spinor equation.

Classified solutions on local Riemannian products, Sasakian manifolds, and 3-dimensional flows.

Abstract

We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those Riemannian flows $M$ carrying non-trivial solutions to that equation in case $M$ is a local Riemannian product, a Sasakian manifold or 3-dimensional.