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Curves of constant breadth according to type-2 bishop frame in E3

Year 2017, Volume: 66 Issue: 1, 206 - 212, 01.02.2017
https://doi.org/10.1501/Commua1_0000000790

Abstract

In this paper, we study the curves of constant breadth accordingto type-2 Bishop frame in the 3-dimensional Euclidean Space E3. Moreoversome characterizations of these curves are obtained

References

  • Bishop L. R., There is More Than one way to Frame a Curve, Am. Math. Monthly, (1975), (3), 246-251.
  • Blaschke W., Konvexe Bereiche gegebener konstanter Breite und kleinsten Inhalts, Math. Ann., (1915), 76(4), 504-513.
  • Euler L., De curvis triangularibus, Acta Acad. Prtropol., (1780), 3-30.
  • Fujivara M., On Space Curves of Constant Breadth, Tohoku Math. J., (1914), 179-184.
  • Gun Bozok H. and Oztekin H., Some characterization of curves of constant breadth according to Bishop frame in E3space, i-managerâs Journal on Mathematics, (2013), 2(3), 7-11.
  • Gluck, H., Higher curvatures of curves in Euclidean space, Amer. Math. Montly, (1966), 73, 704.
  • Hacisalihoglu H. H. and Ozturk R., On the Characterization of Inclined Curves in En, I. Tensor, N.S. (2003), 64, 163-170.
  • Hacisalihoglu H. H., Diğerential Geometry, Ankara University Faculty of Science, 2000.
  • Kazaz M., Onder M. and Kocayigit H., Spacelike curves of constant breadth in Minkowski space, Int. J. Math. Anal., (2008), 2(22), 1061-1068.
  • Kose O., On space curves of constant breadth, Doga Mat., (1986), 10(1), 11-14.
  • Magden A . and Kose O., On the curves of constant breadth in E4space, Turkish J. Math., (1997), 21(3), 277-284.
  • Mellish, A. P., Notes on diğerential geometry, Ann. of Math., (1931), 32(1), 181-190.
  • Ozyilmaz E., Classical diğerential geometry of curves according to type-2 bishop trihedra, Mathematical and Computational Applications, (2011), 16(4), 858-867.
  • Reuleaux F., The Kinematics of Machinery, Trans. By A. B. W. Kennedy, Dover, Pub. Nex York, 1963.
  • Sezer M., Diğerential equations characterizing space curves of constant breadth and a criterion for these curves, Doga Mat., (1989), 13(2), 70-78.
  • Struik D. J., Diğerential geometry in the large, Bull. Amer. Math. Soc., (1931), 37(2), 49-62.
  • Tanaka H., Kinematics Design of Cam Follower Systems, Doctoral Thesis, Columbia Univ., Yilmaz S. and Turgut M., Partially null curves of constant breadth in semi-Riemannian space, Modern Applied Science, (2009), 3(3), 60-63.
  • Yilmaz S. and Turgut M., A new version of Bishop frame and an application to spherical images, J. Math. Anal. Appl., (2010), 371, 764-776.
  • Yoon D. W., Curves of constant breadth in Galilean 3-space, Applied Mathematical Sciences, (2014), 8(141), 7013-7018.
Year 2017, Volume: 66 Issue: 1, 206 - 212, 01.02.2017
https://doi.org/10.1501/Commua1_0000000790

Abstract

References

  • Bishop L. R., There is More Than one way to Frame a Curve, Am. Math. Monthly, (1975), (3), 246-251.
  • Blaschke W., Konvexe Bereiche gegebener konstanter Breite und kleinsten Inhalts, Math. Ann., (1915), 76(4), 504-513.
  • Euler L., De curvis triangularibus, Acta Acad. Prtropol., (1780), 3-30.
  • Fujivara M., On Space Curves of Constant Breadth, Tohoku Math. J., (1914), 179-184.
  • Gun Bozok H. and Oztekin H., Some characterization of curves of constant breadth according to Bishop frame in E3space, i-managerâs Journal on Mathematics, (2013), 2(3), 7-11.
  • Gluck, H., Higher curvatures of curves in Euclidean space, Amer. Math. Montly, (1966), 73, 704.
  • Hacisalihoglu H. H. and Ozturk R., On the Characterization of Inclined Curves in En, I. Tensor, N.S. (2003), 64, 163-170.
  • Hacisalihoglu H. H., Diğerential Geometry, Ankara University Faculty of Science, 2000.
  • Kazaz M., Onder M. and Kocayigit H., Spacelike curves of constant breadth in Minkowski space, Int. J. Math. Anal., (2008), 2(22), 1061-1068.
  • Kose O., On space curves of constant breadth, Doga Mat., (1986), 10(1), 11-14.
  • Magden A . and Kose O., On the curves of constant breadth in E4space, Turkish J. Math., (1997), 21(3), 277-284.
  • Mellish, A. P., Notes on diğerential geometry, Ann. of Math., (1931), 32(1), 181-190.
  • Ozyilmaz E., Classical diğerential geometry of curves according to type-2 bishop trihedra, Mathematical and Computational Applications, (2011), 16(4), 858-867.
  • Reuleaux F., The Kinematics of Machinery, Trans. By A. B. W. Kennedy, Dover, Pub. Nex York, 1963.
  • Sezer M., Diğerential equations characterizing space curves of constant breadth and a criterion for these curves, Doga Mat., (1989), 13(2), 70-78.
  • Struik D. J., Diğerential geometry in the large, Bull. Amer. Math. Soc., (1931), 37(2), 49-62.
  • Tanaka H., Kinematics Design of Cam Follower Systems, Doctoral Thesis, Columbia Univ., Yilmaz S. and Turgut M., Partially null curves of constant breadth in semi-Riemannian space, Modern Applied Science, (2009), 3(3), 60-63.
  • Yilmaz S. and Turgut M., A new version of Bishop frame and an application to spherical images, J. Math. Anal. Appl., (2010), 371, 764-776.
  • Yoon D. W., Curves of constant breadth in Galilean 3-space, Applied Mathematical Sciences, (2014), 8(141), 7013-7018.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Hülya Gün Bozok This is me

Sezin Aykurt Sepet This is me

Mahmut Ergüt This is me

Publication Date February 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 1

Cite

APA Gün Bozok, H., Aykurt Sepet, S., & Ergüt, M. (2017). Curves of constant breadth according to type-2 bishop frame in E3. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 206-212. https://doi.org/10.1501/Commua1_0000000790
AMA Gün Bozok H, Aykurt Sepet S, Ergüt M. Curves of constant breadth according to type-2 bishop frame in E3. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2017;66(1):206-212. doi:10.1501/Commua1_0000000790
Chicago Gün Bozok, Hülya, Sezin Aykurt Sepet, and Mahmut Ergüt. “Curves of Constant Breadth According to Type-2 Bishop Frame in E3”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 1 (February 2017): 206-12. https://doi.org/10.1501/Commua1_0000000790.
EndNote Gün Bozok H, Aykurt Sepet S, Ergüt M (February 1, 2017) Curves of constant breadth according to type-2 bishop frame in E3. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 206–212.
IEEE H. Gün Bozok, S. Aykurt Sepet, and M. Ergüt, “Curves of constant breadth according to type-2 bishop frame in E3”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 1, pp. 206–212, 2017, doi: 10.1501/Commua1_0000000790.
ISNAD Gün Bozok, Hülya et al. “Curves of Constant Breadth According to Type-2 Bishop Frame in E3”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (February 2017), 206-212. https://doi.org/10.1501/Commua1_0000000790.
JAMA Gün Bozok H, Aykurt Sepet S, Ergüt M. Curves of constant breadth according to type-2 bishop frame in E3. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:206–212.
MLA Gün Bozok, Hülya et al. “Curves of Constant Breadth According to Type-2 Bishop Frame in E3”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 1, 2017, pp. 206-12, doi:10.1501/Commua1_0000000790.
Vancouver Gün Bozok H, Aykurt Sepet S, Ergüt M. Curves of constant breadth according to type-2 bishop frame in E3. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):206-12.

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

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