Isometric embeddings of families of special Lagrangian submanifolds

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dc.creatorMatessi, Diego
dc.date2005-03-23
dc.date.accessioned2026-07-07T05:18:16Z
dc.date.available2026-07-07T05:18:16Z
dc.descriptionWe prove that certain Riemannian manifolds can be isometrically embedded inside Calabi-Yau manifolds. For example we prove that given any real-analytic one parameter family of Riemannian metrics $g_t$ on a 3-dimensional manifold $Y$ with volume form independent of $t$ and with a real-analytic family of nowhere vanishing harmonic one forms $θ_t$, then $(Y, g_t)$ can be realized as a family of special Lagrangian submanifolds of a Calabi-Yau manifold $X$. We also prove that certain principal torus bundles can be equivariantly and isometrically embedded inside Calabi-Yau manifolds with torus action. We use this to construct examples of $n$-parameter families of special Lagrangian tori inside $n+k$-dimensional Calabi-Yau manifolds with torus symmetry. We also compute McLean's metric of 3-dimensional special Lagrangian fibrations with $T^2$-symmetry.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math/0503494
dc.identifierhttp://arxiv.org/abs/math/0503494
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74605
dc.subjectDifferential Geometry
dc.subject53c38, 53c25
dc.titleIsometric embeddings of families of special Lagrangian submanifolds
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