Caustics of pseudo-spherical surfaces in the Euclidean 3-space
- 27 June 2023
- journal article
- research article
- Published by Walter de Gruyter GmbH in Forum Mathematicum
- Vol. 36 (1) , 21-32
Abstract
We study geometric properties of caustics of pseudo-spherical surfaces, that is, surfaces with constant negative Gaussian curvature -1 in the Euclidean 3-space . We investigate the Gaussian and the mean curvature of caustics of pseudo-spherical surfaces. Moreover, a certain condition required for the caustics to be minimal surfaces is derived.
Keywords
Funding Information
- Japan Society for the Promotion of Science (JP19K14533)
- Japan Society for the Promotion of Science (JP22K13914)
- Japan Society for the Promotion of Science (JP20H01801)
- Japan Society for the Promotion of Science (JP22KK0034)
- Japan Society for the Promotion of Science (JPJSBP1 20190103)
This publication has 30 references indexed in Scilit:
- Criteria for $D_4$ singularities of wave frontsTohoku Mathematical Journal, 2011
- Horospherical flat surfaces in Hyperbolic 3-spaceJournal of the Mathematical Society of Japan, 2010
- The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and "flat" spacelike surfacesJournal of Singularities, 2010
- A
k
singlarities of wave frontsMathematical Proceedings of the Cambridge Philosophical Society, 2009
- The geometry of frontsAnnals of Mathematics, 2009
- Singularities of flat fronts in hyperbolic spacePacific Journal of Mathematics, 2005
- Singularities of line congruencesProceedings of the Royal Society of Edinburgh: Section A Mathematics, 2003
- Application of soliton theory to the construction of pseudospherical surfaces in R3Annals of Global Analysis and Geometry, 1993
- An analogue of Bäcklund's theorem in affine geometryRocky Mountain Journal of Mathematics, 1980
- Ueber Flächen von constanter Gaussscher KrümmungTransactions of the American Mathematical Society, 1901