Holomorphic vector fields and minimal Lagrangian submanifolds

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dc.creatorGoldstein, Edward
dc.date2000-10-20
dc.date.accessioned2026-07-07T04:38:09Z
dc.date.available2026-07-07T04:38:09Z
dc.descriptionThe purpose of this note is to establish the following theorem: Let N be a Kahler manifold, L be a compact oriented immersed minimal Lagrangian submanifold in N and V be a holomorphic vector field in a neighbourhood of L in N. Let div(V) be the (complex) divergence of V. Then the integral of div(V) over L is 0. Vice versa let N^2n be Kahler-Einstein with non-zero scalar curvature and L^n be a totally real oriented embedded n-dimensional real-analytic submanifold of N s.t. the divergence of any holomorphic vector field defined in a neighbourhood of L in N integrates to 0 on L. Then L is a minimal Lagrangian submanifold of N.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math/0010203
dc.identifierhttp://arxiv.org/abs/math/0010203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60172
dc.subjectDifferential Geometry
dc.subject53XX
dc.titleHolomorphic vector fields and minimal Lagrangian submanifolds
dc.typetext

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