Abstract
We 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 three-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.
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Mathematics Subject Classification (2000): 53-XX, 53C38.
Communicated by N. Hitchin (Oxford)
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Matessi, D. Isometric Embeddings of Families of Special Lagrangian Submanifolds. Ann Glob Anal Geom 29, 197–220 (2006). https://doi.org/10.1007/s10455-005-9008-2
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DOI: https://doi.org/10.1007/s10455-005-9008-2