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Year 1998, Volume: 47 , 0 - 0, 01.01.1998
https://doi.org/10.1501/Commua1_0000000404

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  • Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi

On general helices and pseudo-riemannian manifolds

Year 1998, Volume: 47 , 0 - 0, 01.01.1998
https://doi.org/10.1501/Commua1_0000000404

Abstract

In a Riemannian manifold, a regular curve is called a general helix if is constant and its firs and second curvatures are not constant [4]. İf its First and second curvatures are constant the third curvature is zero then the regular curve is called helix. For helices in a Lorentzian manifold, there is a research of T. Ikawa, who investigated and obtained the differential equation;
D D D X = KD X , (K = a - p5
XXX X
fOT the drcular helix which corresponds to the case that the curvatures a and P of the timelike curve c(t) on the Lorentzian manifold M are constant [3], Later, N. Ekmekçi and H.H. HacısaUhoğlu obtained the differential equation I\I\DxX = KD^K + 3a' D^Y ,
K = of + a2 P')
P
fcff the case of general helix [2]. Recently, T. Nakanishi [5] prove the following lemma about a helix in Pseudo-Riemannian manifold which is stated as, “A unit speed curve c in M is a helix if and only if there exist a constant X such that D D D X = XD X”
XXX X
a
îhis paper generalizes the lemma stated above lo the case of a general helix.

References

  • Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

N. Ekmekçi This is me

Publication Date January 1, 1998
Submission Date January 1, 1998
Published in Issue Year 1998 Volume: 47

Cite

APA Ekmekçi, N. (1998). On general helices and pseudo-riemannian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 47. https://doi.org/10.1501/Commua1_0000000404
AMA Ekmekçi N. On general helices and pseudo-riemannian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. January 1998;47. doi:10.1501/Commua1_0000000404
Chicago Ekmekçi, N. “On General Helices and Pseudo-Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 47, January (January 1998). https://doi.org/10.1501/Commua1_0000000404.
EndNote Ekmekçi N (January 1, 1998) On general helices and pseudo-riemannian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 47
IEEE N. Ekmekçi, “On general helices and pseudo-riemannian manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 47, 1998, doi: 10.1501/Commua1_0000000404.
ISNAD Ekmekçi, N. “On General Helices and Pseudo-Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 47 (January 1998). https://doi.org/10.1501/Commua1_0000000404.
JAMA Ekmekçi N. On general helices and pseudo-riemannian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1998;47. doi:10.1501/Commua1_0000000404.
MLA Ekmekçi, N. “On General Helices and Pseudo-Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 47, 1998, doi:10.1501/Commua1_0000000404.
Vancouver Ekmekçi N. On general helices and pseudo-riemannian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1998;47.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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