Dr Wilhelm Klingenberg's Outputs (3)

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.