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Outputs (34)

Geodesic Flow on Global Holomorphic Sections of TS^2 (2007)
Journal Article
Klingenberg, W., & Guilfoyle, B. (2007). Geodesic Flow on Global Holomorphic Sections of TS^2. Bulletin of the Belgian Mathematical Society Simon Stevin (Printed), 14(2), 363-371

We study the geodesic flow on the global holomorphic sections of the bundle π:TS2→S2π:TS2→S2 induced by the neutral Kähler metric on the space of oriented lines of R3R3, which we identify with TS2TS2. This flow is shown to be completely integrable wh... Read More about Geodesic Flow on Global Holomorphic Sections of TS^2.

Isolated umbilic points on surfaces in R^3 (2006)
Journal Article
Klingenberg, W., & Guilfoyle, B. (2006). Isolated umbilic points on surfaces in R^3. Deltio tīs Ellīnikīs mathīmatikīs etaireias (1960), 51, 23-30

Reflection of a wave off a surface. (2006)
Journal Article
Klingenberg, W., & Guilfoyle, B. (2006). Reflection of a wave off a surface. Journal of Geometry, 84(1), 55-72. https://doi.org/10.1007/s00022-005-0022-0

Recent investigations of the space of oriented lines in R3R3 are applied to geometric optics. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecti... Read More about Reflection of a wave off a surface..

Level sets of functions and symmetry sets of surface sections (2005)
Presentation / Conference Contribution
Diatta, A., Giblin, P., Guilfoyle, B., & Klingenberg, W. (2005, October). Level sets of functions and symmetry sets of surface sections. Presented at Mathematics of Surfaces XI: 11th IMA international conference, Loughborough

We prove that the level sets of a real C s function of two variables near a non-degenerate critical point are of class C [s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at an ellipti... Read More about Level sets of functions and symmetry sets of surface sections.

The Casimir effect between non-parallel plates by geometric optics (2005)
Journal Article
Guilfoyle, B., Klingenberg, W., & Sen, S. (2005). The Casimir effect between non-parallel plates by geometric optics. Reviews in Mathematical Physics, 17(8), 859 - 880. https://doi.org/10.1142/s0129055x05002431

The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ℝ3 to describe the reflection of rays off a surface. This can be viewed as a parametric approach to geometric optics which has m... Read More about The Casimir effect between non-parallel plates by geometric optics.

An indefinite Kaehler metric on the space of oriented lines (2005)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2005). An indefinite Kaehler metric on the space of oriented lines. Journal of the London Mathematical Society, 72(2), 497-509. https://doi.org/10.1112/s0024610705006605

The total space of the tangent bundle of a Kähler manifold admits a canonical Kähler structure. Parallel translation identifies the space ${\mathbb{T}}$ of oriented affine lines in ${\mathbb{R}}^3$ with the tangent bundle of $S^2$. Thus the round met... Read More about An indefinite Kaehler metric on the space of oriented lines.

Generalized surfaces in R^3 (2004)
Journal Article
Klingenberg, W., & Guilfoyle, B. (2004). Generalized surfaces in R^3. Mathematical Proceedings of the Royal Irish Academy, 104A(2), 199-209

On the space of oriented affine lines in R^3 (2004)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2004). On the space of oriented affine lines in R^3. Archiv der Mathematik, 82(1), 81 - 84. https://doi.org/10.1007/s00013-003-4861-3

We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in, as we illustrate wi... Read More about On the space of oriented affine lines in R^3.