Outputs (20)

A First Course in Differential Geometry (2018)
Book
Woodward, L., & Bolton, J. (2018). A First Course in Differential Geometry. Cambridge University Press

This book, which is aimed at senior undergraduate students, provides an introduction to the differential geometry of surfaces in Euclidean space. Topics include Gaussian curvature, Theorema Egregium, geodesics, Gauss-Bonnet Theorem. There is a final... Read More about A First Course in Differential Geometry.

Transforms for minimal surfaces in the 5-sphere (2007)
Journal Article
Bolton, J., & Vrancken, L. (2009). Transforms for minimal surfaces in the 5-sphere. Differential Geometry and its Applications, 27(1), 34-46. https://doi.org/10.1016/j.difgeo.2008.06.005

We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how to associa... Read More about Transforms for minimal surfaces in the 5-sphere.

The space of harmonic two-spheres in the unit four-sphere (2006)
Journal Article
Bolton, J., & Woodward, L. (2006). The space of harmonic two-spheres in the unit four-sphere. Tohoku mathematical journal, 58(2), 231-236. https://doi.org/10.2748/tmj/1156256402

A harmonic map of the Riemann sphere into the unit 4-dimensional sphere has area 4 pi d for some positive integer d, and it is well-known that the space of such maps may be given the structure of a complex algebraic variety of dimension 2d+4. When d... Read More about The space of harmonic two-spheres in the unit four-sphere.

Ruled minimal Lagrangian submanifolds of complex projective 3-space (2005)
Journal Article
Bolton, J., & Vrancken, L. (2005). Ruled minimal Lagrangian submanifolds of complex projective 3-space. Asian Journal of Mathematics, 9(1), 45-56. https://doi.org/10.4310/ajm.2005.v9.n1.a4

We show how a ruled minimal Lagrangian submanifold of complex projective 3-space may be used to construct two related minimal surfaces in the 5-sphere.

Toda equations and Pluecker formulae (2003)
Journal Article
Bolton, J., & Woodward, L. (2003). Toda equations and Pluecker formulae. Bulletin of the London Mathematical Society, 35(2), 145-151. https://doi.org/10.1112/s0024609302001716

An extension is obtained to certain maps into full flag manifolds of compact simple Lie groups of the classical Pluecker formulae for holomorphic curves in complex projectuive space.

From certain Lagrangian minimal submanifolds of the 3-dimensional complex projective space to minimal surfaces in the 5-sphere. (2002)
Journal Article
Bolton, J., Scharlach, C., Vrancken, L., & Woodward, L. (2002). From certain Lagrangian minimal submanifolds of the 3-dimensional complex projective space to minimal surfaces in the 5-sphere. Bulletin of the Australian Mathematical Society, 66(3), 465-475

The Toda equations and equiharmonic maps of surfaces into flag manifolds (2002)
Presentation / Conference Contribution
Bolton, J. (2002, December). The Toda equations and equiharmonic maps of surfaces into flag manifolds

From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space (2002)
Journal Article
Bolton, J., Scharlach, C., & Vrancken, L. (2002). From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space. Bulletin of the Australian Mathematical Society, 66, 465-475

Linearly full harmonic 2-spheres in S^4 of area 20\pi (2001)
Journal Article
Bolton, J., & Woodward, L. (2001). Linearly full harmonic 2-spheres in S^4 of area 20\pi. International Journal of Mathematics, 12(5), 535-554. https://doi.org/10.1142/s0129167x01000915

We give an explicit description of all harmonic 2-spheres of area 20\pi in the round 4-sphere S^4 in terms of their branch points and umbilics. This is obtained by finding canonical forms for the twistor lifts of such maps in complex projective 3-spa... Read More about Linearly full harmonic 2-spheres in S^4 of area 20\pi.

Higher Singularities and the Twistor Fibration π: CP3 → S4 (2000)
Journal Article
Bolton, J., & Woodward, L. (2000). Higher Singularities and the Twistor Fibration π: CP3 → S4. Geometriae Dedicata, 80(1-3), 231-246. https://doi.org/10.1023/a%3A100525941

We use the Klein correspondences to write down an explicit relationship between two holomorphic curves, namely the directrix curve and the twistor lift, associated to a superminimal map from a Riemann surface to the 4-sphere. We also explain how the... Read More about Higher Singularities and the Twistor Fibration π: CP3 → S4.