SU(3)-structures and Special Lagrangian Geometries

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dc.creatorXu, Feng
dc.date2006-10-17
dc.date.accessioned2026-07-07T07:29:09Z
dc.date.available2026-07-07T07:29:09Z
dc.descriptionWe generalize Calabi-Yau 3-folds from the special Lagrangian perspective. More precisely, we study SU(3)-structures which admit as "nice" a local special Lagrangian geometry as the flat $\mathbf{C}^3$ or a Calabi-Yau structure does. The underlying almost complex structure may not be integrable. Such SU(3)-structures are called {\it admissible}. Among these, we are particularly interested in a subclass of SU(3)-structures called {\it nearly Calabi-Yau}. We discuss the local generalities of admissible SU(3)-structures and nearly Calabi-Yau structures in Cartan's sense. Examples of nearly Calabi-Yau but non-Calabi-Yau structures as well as other admissible SU(3)-structures are constructed from the twistor spaces of self-dual Einstein 4-manifolds. Two classes of examples of complete special Lagrangian submanifolds are found by considering the anti-complex involution of the underlying SU(3)-structures. We finally show that the moduli space of compact special Lagrangian submanifolds in a nearly Calabi-Yau manifold behaves in the same way as the moduli in the Calabi-Yau case.
dc.description31 pages
dc.identifierhttps://arxiv.org/abs/math/0610532
dc.identifierhttp://arxiv.org/abs/math/0610532
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117998
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject53C38
dc.titleSU(3)-structures and Special Lagrangian Geometries
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