Powiadomienia systemowe
- Sesja wygasła!
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We say that a surface in Minkowski 3-space is a lightlike developable if all pseudo-normal vectors of the regular part of the surface are lightlike. The tangent surface of a lightlike curve is one of the lightlike developables. We give a generic classification of such surfaces. The all arguments in this paper are elementary. However, we discovered the H3 type singularity appears in generic for such a class of surfaces. Since the H3 type singularity usually appears in non-generic situation, this is a quite interesting phenomenon.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
387--399
Opis fizyczny
Bibliogr. 14 poz., rys.
Twórcy
autor
autor
- Department of Mathematics Hokkaido University Sapporo 060-0810 Japan, izumiya@math.sci.hokudai.ac.jp
Bibliografia
- [1] S. Chandrasekhar, The Mathematical Theory of Black Holes, International Series of Monographs on Physics 69, Oxford Univeristy Press, 1983.
- [2] J. P. Cleave, The form of the tangent developable at points of zero torsion on space curves, Math. Proc. Cambridge Philos. Soc. 88 (1980), 403–407.
- [3] M. Golubitsky, V. Guillemin, Stable Mappings and their Singularities, Springer GTM 14 (1973).
- [4] G. Ishikawa, Determinacy of envelope of the osculating hyperplanes to a curve, Bull. London Math. Soc. 25 (1993), 603–610.
- [5] G. Ishikawa, Developable of a curve and determinacy relative to osculation-type, Quart. J. Math. Oxford 46 (1995), 437–451.
- [6] S. Izumiya, D. Pei, T. Sano, The lightcone Gauss map and the lightcone developable of a spacelike curve in Minkowski 3-space, Glasgow Math. J. 42 (2000), 75–89.
- [7] S. Izumiya, N. Takeuchi, Geometry of Ruled Surfaces, Applicable Mathematics in the Golden Age, Ed. by J. C. Misra, Narosa Publishing House (2003).
- [8] C. W. Misner, K. S. Thorne, J. W. Wheeler, Gravitation, W. H. Freeman and Co., San Francisco, CA (1973).
- [9] D. Mond, On the tangent developable of a space curve, Math. Proc. Cambridge Philos. Soc. 91 (1982), 351–355.
- [10] D. Mond, Singularities of the tangent developable surface of a space curve, Quart. J. Math. Oxford 40 (1989), 79-91.
- [11] D. Pei, Singularities of RP2-valued Gauss maps of surfaces in Minkowski 3-space, Hokkaido Math. J. 28 (1999), 97–115.
- [12] O. P. Scherbak, Wavefront and reflection groups, Russian Math. Surveys 43-3 (1988), 149–194.
- [13] O. P. Scherbak, Projectively dual space curves and Legendre singularities, Trudy Tbiliss. Univ. 232-233 (1982), 280–336.
- [14] I. Vaisman, A first course in differential geometry, Pure and Applied Mathematics. A series of Monograph and Textbooks, Marcel Dekker, (1984).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0032-0006