Genuine Deformations of Submanifolds
نویسندگان
چکیده
منابع مشابه
Deformations of Calibrated Submanifolds
Assuming the ambient manifold is KK ahler, the theory of complex sub-manifolds can be placed in the more general context of calibrated submanifolds, see HL]. It is therefore natural to try to extend some of the many results in complex geometry to the other calibrated geometries of HL]. In particular, the question of deformability of calibrated submanifolds is addressed here (analogous to Kodair...
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Let L be a special Lagrangian submanifold of R with boundary lying on the symplectic, codimension 2 submanifold W . It is shown how deformations of L which keep the boundary of L confined to W can be described by an elliptic boundary value problem, and two results about minimal Lagrangian submanifolds with boundary are derived using this fact. The first is that the space of minimal Lagrangian s...
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Let M be a compact smooth manifold of holonomy G2. We prove that the space of infinitesimal associative deformations of a compact associative submanifold Y with boundary in a coassociative submanifold X is the solution space of an elliptic problem. Further, we compute its virtual dimension. For ∂Y connected it is given by ∫ ∂Y c1(νX)+ 1− g, where g denotes the genus of ∂Y , νX the orthogonal co...
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The naive approach is to parametrize these deformations as the zero-set of a “mean curvature operator”, then study them using the implicit function theorem. However, this entails a good understanding of the Jacobi operator of the initial submanifold Σ, which in general is not possible. The work of Oh and, more recently, of McLean (cfr. [Oh], [ML]) shows that, in the “right” geometric context, t...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2004
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2004.v12.n5.a6