Equivariant gluing constructions of contact stationary
نویسنده
چکیده
A contact-stationary Legendrian submanifold of S2n+1 is a Legendrian submanifold whose volume is stationary under contact deformations. The simplest contactstationary Legendrian submanifold (actually minimal Legendrian) is the real, equatorial n-sphere S0. This paper develops a method for constructing contact-stationary (but not minimal) Legendrian submanifolds of S2n+1 by gluing together configurations of sufficiently many U (n + 1)-rotated copies of S0. Two examples of the construction, corresponding to finite cyclic subgroups ofU (n+1) are given. The resulting submanifolds are very symmetric; are geometrically akin to a ‘necklace’ of copies of S0 attached to each other by narrow necks and winding a large number of times around S2n+1 before closing up on themselves; and are topologically equivalent to S1 × Sn−1. Mathematics Subject Classification (2000) 58Jxx · 53Axx
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Equivariant Gluing Constructions of Contact Stationary Legendrian Submanifolds in S
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