Characterizations of space curves with 1-type Darboux instantaneous rotation vector
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this study, by using Laplace and normal Laplace operators, we give some characterizations for the Darboux instantaneous rotation vector field of the curves in the Euclidean 3-space $E^{3} $. Further, we give necessary and sufficient conditions for unit speed space curves to have 1-type Darboux vectors. Moreover, we obtain some characterizations of helices according to Darboux vector.
Abstract
In this study, by using Laplace and normal Laplace operators, we give some characterizations for the Darboux instantaneous rotation vector field of the curves in the Euclidean 3-space $E^{3} $. Further, we give necessary and sufficient conditions for unit speed space curves to have 1-type Darboux vectors. Moreover, we obtain some characterizations of helices according to Darboux vector.
참고문헌 (11)
- B. Y. Chen, "Biharmonic surface in pseudo-Euclidean spaces", Mem. Fac. Sci. Kyushu Univ. Ser. A, 45(2), pp.323~347 (1991)
- A. Ferrandez, "Biharmonic Hopf cylinders", Rocky Monutain J. Math, 28(3), pp.957~975 (1998)
- H. H. Hacısalihoglu, "On the characterization of inclined curves in En. I", Tensor, N. S, 64, pp.157~162 (2003)
- H. H. Hacısalihoglu, "On the characterization of inclined curves in En. II", Tensor, N. S, 64, pp.163~169 (2003)
- K. Ilarslan, "Some special curves on Non-Euclidean manifolds", Ph.D., pp.2002
- H. Kocayigit, "Lorentz Manifoldlarında Biharmonik Egriler ve Kontak Geometri", Ph.D, pp.2004
- H. Kocayigit, "1-type and biharmonic Frenet curves in Lorentzian 3-space", Iran. J. Sci. Technol. Trans. A Sci, 33(2), pp.159~168 (2009)
- H. Kocayigit, "1-type and biharmonic curves in Euclidean 3-space", Int. Electron. J. Geom, 4(1), pp.97~101 (2011)
- H. Kocayigit, "Characterizations of Curves in E2n+1 with 1-type Darboux Vector", Math. Morav, 17(2), pp.29~37 (2013)
- M. Petrovic-Torgasev, "W-curves in Minkowski space-time", Novi Sad J. Math, 32(2), pp.55~65 (2002)
- D. J. Struik, "Lectures on Classical Differential Geometry" (1988), Addison Wesley