A note on the Ricci scalar of six dimensional manifold with SU(2) structure
Gautier Solard
TL;DR
This paper derives a formula for the Ricci scalar of six-dimensional manifolds with SU(2) structure by analyzing intrinsic torsion, extending previous SU(3) results to SU(2) cases.
Contribution
It provides a new explicit expression for the Ricci scalar in terms of torsion classes for six-dimensional SU(2) structure manifolds, inspired by prior SU(3) findings.
Findings
Derived a formula for Ricci scalar using torsion classes
Extended SU(3) results to SU(2) structures
Provides tools for studying geometry in string theory contexts
Abstract
Taking [math/0606786] as an inspiration, we study the intrinsic torsion of a SU(2) structure manifold in six dimensions to give a formula for the Ricci scalar in terms of torsion classes. The derivation is founded on the SU(3) result coming from the aforementioned paper.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Black Holes and Theoretical Physics