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2004•The Quarterly Journal of MathematicsRequires access

On a new construction of special Lagrangian immersions in complex Euclidean space

Ildefonso Castro

Open publisher page 14 citations

Abstract

We construct new special Lagrangian submanifolds in complex Euclidean space using a pair of minimal Legendrian submanifolds in odd‐dimensional spheres and certain Lagrangian surface belonging to a family that can be considered as a generalization of the special Lagrangian surfaces in complex Euclidean plane. Our examples include those invariant under the standard action of SO(p+1)×SO(q+1) on Cn = Cp+1 ×Cq+1, n=p+q+2.

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What this paper is about

We construct new special Lagrangian submanifolds in complex Euclidean space using a pair of minimal Legendrian submanifolds in odd‐dimensional spheres and certain Lagrangian surface belonging to a family that can be considered as a generalization of the special Lagrangian surfaces in complex Euclidean plane. Our examples include those invariant under the standard action of SO(p+1)×SO(q+1) on Cn = Cp+1 ×Cq+1, n=p+q+2.

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OpenAlex reports 14 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We construct new special Lagrangian submanifolds in complex Euclidean space using a pair of minimal Legendrian submanifolds in odd‐dimensional spheres and certain Lagrangian surface belonging to a family that can be considered as a generalization of the special Lagrangian surfaces in complex Euclidean plane. Our examples include those invariant under the standard action of SO(p+1)×SO(q+1) on Cn = Cp+1 ×Cq+1, n=p+q+2.

Key concepts: Euclidean geometry, Lagrangian, Euclidean space, Space (punctuation), Mathematics, Volume (thermodynamics), Pure mathematics, Computer science

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