Second Order Families of Special Lagrangian Submanifolds in ℂ4
نویسندگان
چکیده
منابع مشابه
2 00 3 Second Order Families of Special Lagrangian Submanifolds in C
This paper extends to dimension 4 the results in the article " Second Order Families of Special Lagrangian 3-folds " by Robert Bryant. We consider the problem of classifying the special Lagrangian 4-folds in C 4 whose fundamental cubic at each point has a nontrivial stabilizer in SO(4). Points on special Lagrangian 4-folds where the SO(4)-stabilizer is nontrivial are the analogs of the umbilica...
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A second order family of special Lagrangian submanifolds of C m is a family characterized by the satisfaction of a set of pointwise conditions on the second fundamental form. For example, the set of ruled special Lagrangian submanifolds of C 3 is characterized by a single algebraic equation on the second fundamental form. While the ‘generic’ set of such conditions turns out to be incompatible, ...
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Special Lagrangian submanifolds may be defined as those submanifolds which are both Lagrangian (an order 1 condition) and minimal (an order 2 condition). Alternatively, they are characterised as those submanifolds which are calibrated by a certain n-form (cf [HL]), so they have the remarkable property of being area minimizing. Their study have received many attention recently since connections ...
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Let M1 and M2 be special Lagrangian submanifolds of a compact Calabi-Yau manifold X that intersect transversely at a single point. We can then think of M1∪M2 as a singular special Lagrangian submanifold of X with a single isolated singularity. We investigate when we can regularize M1 ∪ M2 in the following sense: There exists a family of Calabi-Yau structures Xα on X and a family of special Lagr...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2003
ISSN: 0022-040X
DOI: 10.4310/jdg/1090511687