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大学・研究所にある論文を検索できる 「CURVES IN A SPACELIKE HYPERSURFACE IN MINKOWSKI SPACE-TIME」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。
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CURVES IN A SPACELIKE HYPERSURFACE IN MINKOWSKI SPACE-TIME

Izumiya, Shyuichi 大阪大学 DOI:10.18910/84959

2021.10

概要

In mathematical physics, Minkowski space (or Minkowski space-time) is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold.

The hyperbolic surface and de Sitter surface of a curve are defined in the spacelike hyper- surface M in Minkowski 4-space and located, respectively, in hyperbolic 3-space and de Sitter 3-space. In this study, techniques from singularity theory were applied to obtain the generic shape of such surfaces and their singular value sets and the geometrical meanings of these singularities were investigated.

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参考文献

[1] J.W. Bruce and P.J. Giblin: Curves and Singularities, a geometrical introduction to singularity theory, Cambridge University Press, Cambridge, 1992.

[2] S. Hananoi, N. Ito and S. Izumiya: Spherical Darboux images of curves on surfaces, Beitra¨ge zur Algebra und Geometrie/Contributions to Algebra and Geometry, (2015), 1–11.

[3] R. Hayashi, S. Izumiya and T. Sato: Focal surfaces and evolutes of curves in hyperbolic space, Commun. Korean Math. Soc. 32 (2017), 147–163.

[4] S. Izumiya, A.C. Nabarro and A.J. Sacramento: Horospherical and hyperbolic dual surfaces of spacelike curves in de Sitter space, J. Singul. 16 (2017), 180–193.

[5] S. Izumiya, A.C. Nabarro and A.J. Sacramento: Pseudo-spherical normal Darboux images of curves on a timelike surface in three dimensional Lorentz-Minkowski space, J. Geom. Phys. 97 (2015), 105–118.

[6] S. Izumiya, K. Saji and M. Takahashi: Horospherical flat surfaces in hyperbolic 3-space, J. Math. Soc. Japan 62 (2010), 789–849.

[7] S. Izumiya and T. Sato: Lightlike hypersurface along spacelike submanifolds in Minkowski space-time, J. Geom. Phys. 71 (2013), 30–52.

[8] A.C. Nabarro and A.J. Sacramento: Focal set of curves in the Minkowski space near lightlike points, Publ. Math. Debrecen 88 (2016), 487–510.

[9] J.G. Ratcliffe: Foundations of hyperbolic manifolds, Graduate texts in Mathematics 149, Springer, New York, 2006.

[10] T. Sato: Pseudo-spherical evolutes of curves on a spacelike surface in three dimensional, Lorentz- Minkowski space, J. Geom 103 (2012), 319–331.

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