Equivariant Gluing Constructions of Contact Stationary Legendrian Submanifolds of the (2n+1)-Sphere

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dc.creatorButscher, Adrian
dc.date2006-08-11
dc.date2007-07-03
dc.date.accessioned2026-07-07T08:13:38Z
dc.date.available2026-07-07T08:13:38Z
dc.descriptionA contact stationary Legendrian submanifold of $S^{2n+1}$ 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 $S_0$. This paper develops a method for constructing contact stationary (but not minimal) Legendrian submanifolds of $S^{2n+1}$ by gluing together configurations of sufficiently many $U(n+1)$-rotated copies of $S_0$ at isolated points of suitably transverse intersection. 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 $S^{2n + 1}$ before closing up on itself; and are topologically equivalent to $S^1 \times S^{n-1}$. Moreover, they represent wholly new examples of contact stationary embedded submanifolds of $S^{2n + 1}$ and thus give rise to wholly new examples of embedded Hamiltonian stationary cones in $C^{n+1}$.
dc.description53 Pages. Fully revised and streamlined
dc.identifierhttps://arxiv.org/abs/math/0608275
dc.identifierhttp://arxiv.org/abs/math/0608275
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132838
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject58Jxx (primary) 54Cxx (secondary)
dc.titleEquivariant Gluing Constructions of Contact Stationary Legendrian Submanifolds of the (2n+1)-Sphere
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