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Special Lagrangian Cones in C 3 and Primitive Harmonic Maps
Author(s) -
McIntosh Ian
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004204
Subject(s) - lagrangian , torus , context (archaeology) , harmonic , cone (formal languages) , mathematics , space (punctuation) , harmonic map , mathematical analysis , surface (topology) , pure mathematics , physics , classical mechanics , geometry , computer science , quantum mechanics , algorithm , geology , operating system , paleontology
It is shown that every special Lagrangian cone in C 3 determines, and is determined by, a primitive harmonic surface in the 6‐symmetric space SU 3 /SO 2 . For cones over tori, this allows the classification theory of harmonic tori to be used to describe the construction of all the corresponding special Lagrangian cones. A parameter count is given for the space of these, and some of the examples found recently by Joyce are put into this context.