ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE

Volume: 65 Number: 2 August 1, 2016
  • Hakan Şimşek
  • Mustafa Özdemır
EN

ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE

Abstract

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Keywords

References

  1. B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Inc., London, 1983.
  2. B. J. Papantoniou, Investigation on the smooth surface S of Rthe normals of which, establish a rectilinear congruence such that AK1+ BK2= 0;Tensor, N. S. Vol. 47 (1988).
  3. C. Weihuan, L. Haizhong, Spacelike Weingarten Surfaces in R3and the Sine-Gordon Equa- 1 tion, J ournal of Mathematical Analysis and Applications 214, 459-474 (1997).
  4. D. J. Struik, Lectures on Classical Diğ erential Geometry, Second Edition Dover Publications, INC. New York (1961).
  5. F. Tari, Caustics of surfaces in the Minkowski 3-space, Q. J. Math. 63(1), 189–209 (2012).
  6. G. Tsagas, On the rectilinear congruences whose straight lines are tangent to one parameter family of curves on a surface, Tensor, N. S., 29 (1975), 287-294.
  7. H. ¸Sim¸sek, M. Özdemir, The Sub-Parabolic Lines in the Minkowski 3-Space, Results in Math- ematics, 67, 417-430 (2015), Doi: 10.1007/s00025-014-0409-z.
  8. Hou Zhong Hua, Li li, A kind of rectilinear congruences in the Minkowski 3-Space, Journal of Mathematical Research & Exposition Nov., 2008, Vol. 28, No. 4 pp. 911–918.

Details

Primary Language

English

Subjects

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Journal Section

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Authors

Hakan Şimşek This is me

Mustafa Özdemır This is me

Publication Date

August 1, 2016

Submission Date

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Acceptance Date

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Published in Issue

Year 2016 Volume: 65 Number: 2

APA
Şimşek, H., & Özdemır, M. (2016). ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(2), 55-64. https://doi.org/10.1501/Commua1_0000000759
AMA
1.Şimşek H, Özdemır M. ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(2):55-64. doi:10.1501/Commua1_0000000759
Chicago
Şimşek, Hakan, and Mustafa Özdemır. 2016. “ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 (2): 55-64. https://doi.org/10.1501/Commua1_0000000759.
EndNote
Şimşek H, Özdemır M (August 1, 2016) ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 2 55–64.
IEEE
[1]H. Şimşek and M. Özdemır, “ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 2, pp. 55–64, Aug. 2016, doi: 10.1501/Commua1_0000000759.
ISNAD
Şimşek, Hakan - Özdemır, Mustafa. “ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/2 (August 1, 2016): 55-64. https://doi.org/10.1501/Commua1_0000000759.
JAMA
1.Şimşek H, Özdemır M. ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:55–64.
MLA
Şimşek, Hakan, and Mustafa Özdemır. “ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 2, Aug. 2016, pp. 55-64, doi:10.1501/Commua1_0000000759.
Vancouver
1.Hakan Şimşek, Mustafa Özdemır. ON FOCAL SURFACES FORMED BY TIMELIKE NORMAL RECTILINEAR CONGRUENCE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016 Aug. 1;65(2):55-64. doi:10.1501/Commua1_0000000759

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

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