A construction method produces new special Lagrangian submanifolds L' from existing L in Calabi-Yau manifolds using generalized perpendicular symmetries and non-abelian Lie group moment maps, with examples in Stenzel-metric cotangent bundles of spheres.
Special Lagrangian submanifolds and cohomogeneity one actions on the complex projective space
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abstract
We construct examples of cohomogeneity one special Lagrangian submanifolds in the cotangent bundle over the complex projective space, whose Calabi-Yau structure was given by Stenzel. For each example, we describe the condition of special Lagrangian as an ordinary differential equation. Our method is based on a moment map technique and the classification of cohomogeneity one actions on the complex projective space classified by Takagi.
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math.DG 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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A construction of special Lagrangian submanifolds by generalized perpendicular symmetries
A construction method produces new special Lagrangian submanifolds L' from existing L in Calabi-Yau manifolds using generalized perpendicular symmetries and non-abelian Lie group moment maps, with examples in Stenzel-metric cotangent bundles of spheres.