## Caustic of the three-dimensional ellipsoid. (Caustique de la surface ellipsoïdale à trois dimensions.)(French)Zbl 0951.53002

The authors study the normals of a 3-dimensional ellipsoid in 4-dimensional Euclidean space. The envelope of these normals is called caustic. The authors show, that this caustic is a hypersurface consisting of three parts, which intersect in four closed curves of hyperbolic umbilics. The considerations are based on the co-rank of a suitable mapping which is associated with the normals of the given ellipsoid.
Reviewer: O.Röschel (Graz)

### MSC:

 53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related $$n$$-spaces

### Keywords:

caustic; umbilic; 3-dimensional ellipsoid
Full Text:

### References:

 [1] Arnol’d V. I., ”Singularity theory” (1996) [2] Arnol’d V. I., Singularities of differentiable maps, I: The classification of critical points, caustics and wave fronts (1985) [3] Berry M. V., Physique des defauts (Les Houches, France, 1980) pp 454– (1981) [4] Cayley A., Trans. Camb. Phil. Soc. 12 pp 319– (1873) [5] Chekanov Y. V., Funktsional. Anal, i Prilozhen. 20 (3) pp 66– (1986) [6] Garcia R., An. Acad. Bras. Ciênc. 64 (1992) [7] Garcia R. A., Ann. Global Anal. Geom. 11 (2) pp 185– (1993) · Zbl 0821.53006 [8] Glaser W., Optik 7 pp 96– (1950) [9] Joets A., Europhys. Letters 29 pp 593– (1995) [10] Joets A., Phys. Rev. Lett. 77 pp 1755– (1996) [11] Leisegang S., Optik 10 pp 5– (1953) [12] Porteous I. R., J. Diff. Geom. 5 pp 543– (1971) [13] Poston T., Catastrophe theory and its applications (1978) · Zbl 0382.58006 [14] Thom R., Ann. Inst. Fourier, Grenoble 6 pp 43– (1956) · Zbl 0075.32104
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.