Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones
We study a construction we call the twisted product; in this construction higher dimensional special Lagrangian (SL) and Hamiltonian stationary cones in Cp+q (equivalently special Legendrian or contact stationary submanifolds in S2(p+q)?1) are constructed by combining such objects in Cp and Cq using a suitable Legendrian curve in S3. We study the geometry of these "twisting" curves and in particular the closing conditions for them. In combination with Carberry-McIntosh's continuous families of special Legendrian 2-tori [3] and the authors' higher genus special Legendrians [13], this yields a constellation of new SL and Hamiltonian stationary cones in Cn that are topological products. In particular, for all n sufficiently large we exhibit infinitely many topological types of SL and Hamiltonian stationary cone in Cn, which can occur in continuous families of arbitrarily high dimension. A special case of the twisted product construction yields all SO(p) × SO(q)-invariant SL cones in Cp+q. These SL cones are higher-dimensional analogues of the SO(2)-invariant SL cones constructed previously by Haskins [8, 10] and used in our gluing constructions of higher genus SL cones in C3 [13]. SO(p) × SO(q)-invariant SL cones play a fundamental role as building blocks in gluing constructions of SL cones in high dimensions [14]. We study some basic geometric features of these cones including their closing and embeddedness properties.
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- Nuclear & Particles Physics
- 4904 Pure mathematics
- 0101 Pure Mathematics
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Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Nuclear & Particles Physics
- 4904 Pure mathematics
- 0101 Pure Mathematics