The geometry of SO(p) × SO(q)-invariant special Lagrangian cones

Journal Article (Journal Article)

SO(p) × SO(q)-invariant special Lagrangian cones in ℂp+q(equivalently, SO(p) × SO(q)-invariant special Legendrians in S2(p+q)-1) are an important family of special Lagrangians (SL) whose basic features were studied in our previous paper [13]. In some ways, they play a role analogous to that of Delaunay surfaces in the geometry of CMC surfaces in ℝ3; in particular, they are natural building blocks for our gluing constructions of higher-dimensional SL cones [9, 10, 12]. In this article, we study in detail their geometry paying special attention to features needed in our gluing constructions. In particular, we classify them up to congruence; we determine their full group of symmetries (including various discrete symmetries) in all cases; we prove that many of them are closed and embedded; and finally understand the limiting singular geometry with detailed asymptotics. In understanding the detailed asymptotics a fundamental role is played by a certain conserved quantity (a component of the torque) considered in [13].

Full Text

Duke Authors

Cited Authors

  • Haskins, M; Kapouleas, N

Published Date

  • January 1, 2013

Published In

Volume / Issue

  • 21 / 1

Start / End Page

  • 171 - 205

Electronic International Standard Serial Number (EISSN)

  • 1944-9992

International Standard Serial Number (ISSN)

  • 1019-8385

Digital Object Identifier (DOI)

  • 10.4310/cag.2013.v21.n1.a4

Citation Source

  • Scopus