TY  - JOUR
T1  - ON PARALLEL SURFACES IN MINKOWSKI 3-SPACE
AU  - Unluturk, Yasin
AU  - Ozusaglam, Erdal
PY  - 2013
DA  - December
JF  - TWMS Journal of Applied and Engineering Mathematics
JO  - JAEM
PB  - Işık University Press
WT  - DergiPark
SN  - 2146-1147
SP  - 214
EP  - 222
VL  - 3
IS  - 2
LA  - en
AB  - In this paper, we study on some properties of parallel surfaces in Minkowski  3-space. The results given in this paper were given in Euclidean space by [7, 8]. By  using these two former studies, we show these properties in Minkowski 3-space. Also we  give the relation among the fundamental forms of parallel surfaces in Minkowski 3-space.  Finally we show that how a curve which is geodesic on M become again a geodesic on  parallel surface Mr by the normal map in Minkowski 3-space.
KW  - parallel surfaces
KW  - fundamental forms
KW  - geodesic curve
CR  - [1] C¸ ¨oken, A. C¸., C¸iftci, U. and Ekici, C., 2008, On parallel timelike ruled surfaces with timelike rulings, ¨ Kuwait Journal of Science & Engineering, 35, 21–31.
CR  - [2] Craig, T., Note on parallel surfaces, Journal f¨ur die Reine und Angewandte Mathematik (Crelle’s journal), 94, 162–170., 1883.
CR  - [3] Eisenhart, L.P., 1909, A treatise on the differential geometry of curves and surfaces, Ginn and Company, Boston: New York.
CR  - [4] G¨org¨ul¨u, A. and C¸ ¨oken, C., The dupin indicatrix for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space in semi-Euclidean space R n 1 . Journ. Inst. Math. and Comp. Sci. (Math Series), 7(3), 221-225., 1994.
CR  - [5] A. G¨org¨ul¨u and A. C. C¸ ¨oken, The Euler theorem for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space E n+1 1 , Journ. Inst. Math. and Comp. Sci. (Math. Series) Vol:6, No.2 (1993), 161-165.
CR  - [6] Gray, A., Modern differential geometry of curves and surfaces, CRC Press, Inc., 1993.
CR  - [7] Hacısaliho˘glu, H. H., 2000, Diferensiyel geometri, Cilt I-II, Ankara Universitesi, Fen Fak¨ultesi ¨ Yayınları.
CR  - [8] Hicks, Noel J., Notes on Differential Geometry, Van Nostrant Reinhold Company, London, 1974.
CR  - [9] K¨uhnel, W., 2002, Differential geometry, curves-surfaces-manifolds, American Mathematical Society.
CR  - [10] Lopez, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space, Mini-Course taught at the Instituto de Matematica e Estatistica (IME-USP), University of Sao Paulo, Brasil, 2008
CR  - [11] Nizamoglu, S¸., 1986, Surfaces r´egl´ees parall`eles, Ege Univ. Fen Fak. Derg., 9 (Ser. A), 37-48.  ¨ [12] O’Neill, B., Semi Riemannian geometry with applications to relativity, Academic Press, Inc. New York, 1983.
CR  - [13] Patriciu, A. M., 2010, On some 1,3H3-helicoidal surfaces and their parallel surfaces at a certain distance in 3-dimensional Minkowski space, Annals of the University of Craiova, Maths. and Compt.Science Series, V 37 (4), 93-98.
UR  - https://dergipark.org.tr/en/pub/twmsjaem/article/761412
L1  - https://dergipark.org.tr/en/download/article-file/1179923
ER  -