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Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones

Publication ,  Journal Article
Haskins, M; Kapouleas, N
Published in: Communications in Analysis and Geometry
January 1, 2012

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.

Duke Scholars

Published In

Communications in Analysis and Geometry

DOI

EISSN

1944-9992

ISSN

1019-8385

Publication Date

January 1, 2012

Volume

20

Issue

1

Start / End Page

95 / 162

Related Subject Headings

  • Nuclear & Particles Physics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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Haskins, M., & Kapouleas, N. (2012). Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones. Communications in Analysis and Geometry, 20(1), 95–162. https://doi.org/10.4310/CAG.2012.v20.n1.a4
Haskins, M., and N. Kapouleas. “Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones.” Communications in Analysis and Geometry 20, no. 1 (January 1, 2012): 95–162. https://doi.org/10.4310/CAG.2012.v20.n1.a4.
Haskins M, Kapouleas N. Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones. Communications in Analysis and Geometry. 2012 Jan 1;20(1):95–162.
Haskins, M., and N. Kapouleas. “Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones.” Communications in Analysis and Geometry, vol. 20, no. 1, Jan. 2012, pp. 95–162. Scopus, doi:10.4310/CAG.2012.v20.n1.a4.
Haskins M, Kapouleas N. Closed twisted products and SO(p) × SO(q)-invariant special Lagrangian cones. Communications in Analysis and Geometry. 2012 Jan 1;20(1):95–162.

Published In

Communications in Analysis and Geometry

DOI

EISSN

1944-9992

ISSN

1019-8385

Publication Date

January 1, 2012

Volume

20

Issue

1

Start / End Page

95 / 162

Related Subject Headings

  • Nuclear & Particles Physics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics