Equivariant Gluing Constructions of Contact Stationary Legendrian Submanifolds in S

A contact stationary Legendrian submanifold of S is a Legendrian submanifold whose volume is stationary under contact deformations. The simplest contact stationary Legendrian submanifold (actually minimal and Legendrian) is the real, equatorial n-sphere S0. This paper develops a method for constructing contact stationary (but not minimal) Legendrian submanifolds of S by gluing together configurations of sufficiently many U(n + 1)-rotated copies of S0 at isolated points of suitably transverse intersection. The resulting submanifolds have a large group of symmetries; 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 S before closing up on itself; and are topologically equivalent to S × S.