Equivariant gluing constructions of contact stationary Legendrian submanifolds in $${mathbb {S}^{2n+1}}$$ |
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Authors: | Adrian Butscher |
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Affiliation: | (1) University of Toronto at Scarborough, Toronto, Canada |
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Abstract: | A contact-stationary Legendrian submanifold of is a Legendrian submanifold whose volume is stationary under contact deformations. The simplest contact-stationary Legendrian submanifold (actually minimal Legendrian) is the real, equatorial n-sphere S 0. This paper develops a method for constructing contact-stationary (but not minimal) Legendrian submanifolds of by gluing together configurations of sufficiently many many U(n + 1)-rotated copies of S 0. Two examples of the construction, corresponding to finite cyclic subgroups of U(n + 1) are given. The resulting submanifolds are very symmetric; are geometrically akin to a ‘necklace’ of copies of S 0 attached to each other by narrow necks and winding a large number of times around before closing up on themselves; and are topologically equivalent to . |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000) 58Jxx 53Axx |
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