Isometric Embeddings of Families of Special Lagrangian Submanifolds |
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Authors: | Diego Matessi |
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Institution: | (1) Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale, Via Bellini 25/G, 15100 Alessandria, Italy |
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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.
Mathematics Subject Classification (2000): 53-XX, 53C38.Communicated by N. Hitchin (Oxford) |
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Keywords: | Calabi– Yau manifolds special Lagrangian submanifolds |
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