Emilio Musso : Cauchy-Riemann Geometry of Legendrian Curves in S^3

Let S^3 be the unit 3-sphere with its standard Cauchy–Riemann (CR) structure. We will consider the CR geometry of Legendrian curves in S^3 using the local CR invariants of S^3 thought of as a 3-dimensional CR manifold. More specifically, the focus is on the lower-order cr-invariant variational problem for Legendrian curves in S^3 and on its closed critical curves. The Liouville integrability of such a variational problem will be considered. We discuss the admissible contact isotopy classes of closed critical curves with constant bending. Subsequently, we characterize closed critical curves with non-constant bending in terms of three numerical invariants. In addition, we analyze the geometrical meaning of the numerical invariants in terms of the cr-symmetries of closed critical curves and of the their linking numbers with the symmetry axes.

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Revd Canon Dr Joanna Collicutt: * CANCELLED * ‘Human kind cannot bear very much reality’: the relationship between John Ruskin’s aesthetic theory, spirituality, and mental health

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Dr Elizabeth Powell CANCELLED: CANCELLED Salvation and Loving Regard

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