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Year 2018, , 74 - 79, 26.06.2018
https://doi.org/10.32323/ujma.395094

Abstract

References

  • [1] F. Manhart, Eigentliche Relativsph¨aren, die Regelfla¨chen oder Ru¨ckungsfla¨chen sind, Anz. O¨ sterreich. Akad. Wiss. Math.-Natur. Kl. 125 (1988), 37–40.
  • [2] F. Manhart, Relativgeometrische Kennzeichnungen Euklidischer Hypersph¨aren, Geom. Dedicata 29 (1989), 193–207.
  • [3] H. Pottmann and J. Wallner, Computational Line Geometry, Springer-Verlag, New York, 2001.
  • [4] P. A. Schirokow and A. P. Schirokow, Affine Differentialgeometrie, B. G. Teubner Verlagsgesellschaft, Leipzig, 1962.
  • [5] S. Stamatakis and I. Kaffas, Ruled surfaces asymptotically normalized, J. Geom. Graph. 17 (2013), 177–191.
  • [6] S. Stamatakis, I. Kaffas and I.-I. Papadopoulou, Characterizations of ruled surfaces in R3 and of hyperquadrics in Rn+1 via relative geometric invariants, J. Geom. Graph. 18 (2014), 217–223.
  • [7] S. Stamatakis and I.-I. Papadopoulou, On ruled surfaces relatively normalized, Beitr. Algebra Geom. 58 (2017), 591–605.
  • [8] S. Stamatakis and I.-I. Papadopoulou, Ruled surfaces right normalized, ArXiv:1706.07277 [math.DG].
  • [9] G. Stamou and A.Magkos, Regelefl¨achen relativgeometrisch behandelt, Beitr. Algebra Geom. 45 (2004), 209–215.
  • [10] G. Stamou, S. Stamatakis and I.Delivos, A relative-geometric treatment of ruled surfaces, Beitr. Algebra Geom. 53 (2012), 297–309.

On polar relative normalizations of ruled surfaces

Year 2018, , 74 - 79, 26.06.2018
https://doi.org/10.32323/ujma.395094

Abstract

This paper deals with skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$ which are equipped with polar normalizations, that is, relative normalizations such that the relative normal at each point of the ruled surface lies on the corresponding polar plane. We determine the invariants of a such normalized ruled surface and we study some properties of the Tchebychev vector field and the support vector field of a polar normalization. Furthermore, we study a special polar normalization, the relative image of which degenerates into a curve.

References

  • [1] F. Manhart, Eigentliche Relativsph¨aren, die Regelfla¨chen oder Ru¨ckungsfla¨chen sind, Anz. O¨ sterreich. Akad. Wiss. Math.-Natur. Kl. 125 (1988), 37–40.
  • [2] F. Manhart, Relativgeometrische Kennzeichnungen Euklidischer Hypersph¨aren, Geom. Dedicata 29 (1989), 193–207.
  • [3] H. Pottmann and J. Wallner, Computational Line Geometry, Springer-Verlag, New York, 2001.
  • [4] P. A. Schirokow and A. P. Schirokow, Affine Differentialgeometrie, B. G. Teubner Verlagsgesellschaft, Leipzig, 1962.
  • [5] S. Stamatakis and I. Kaffas, Ruled surfaces asymptotically normalized, J. Geom. Graph. 17 (2013), 177–191.
  • [6] S. Stamatakis, I. Kaffas and I.-I. Papadopoulou, Characterizations of ruled surfaces in R3 and of hyperquadrics in Rn+1 via relative geometric invariants, J. Geom. Graph. 18 (2014), 217–223.
  • [7] S. Stamatakis and I.-I. Papadopoulou, On ruled surfaces relatively normalized, Beitr. Algebra Geom. 58 (2017), 591–605.
  • [8] S. Stamatakis and I.-I. Papadopoulou, Ruled surfaces right normalized, ArXiv:1706.07277 [math.DG].
  • [9] G. Stamou and A.Magkos, Regelefl¨achen relativgeometrisch behandelt, Beitr. Algebra Geom. 45 (2004), 209–215.
  • [10] G. Stamou, S. Stamatakis and I.Delivos, A relative-geometric treatment of ruled surfaces, Beitr. Algebra Geom. 53 (2012), 297–309.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ioanna-Iris Papadopoulou

Stylianos Stamatakis

Publication Date June 26, 2018
Submission Date February 14, 2018
Acceptance Date March 18, 2018
Published in Issue Year 2018

Cite

APA Papadopoulou, I.-I., & Stamatakis, S. (2018). On polar relative normalizations of ruled surfaces. Universal Journal of Mathematics and Applications, 1(2), 74-79. https://doi.org/10.32323/ujma.395094
AMA Papadopoulou II, Stamatakis S. On polar relative normalizations of ruled surfaces. Univ. J. Math. Appl. June 2018;1(2):74-79. doi:10.32323/ujma.395094
Chicago Papadopoulou, Ioanna-Iris, and Stylianos Stamatakis. “On Polar Relative Normalizations of Ruled Surfaces”. Universal Journal of Mathematics and Applications 1, no. 2 (June 2018): 74-79. https://doi.org/10.32323/ujma.395094.
EndNote Papadopoulou I-I, Stamatakis S (June 1, 2018) On polar relative normalizations of ruled surfaces. Universal Journal of Mathematics and Applications 1 2 74–79.
IEEE I.-I. Papadopoulou and S. Stamatakis, “On polar relative normalizations of ruled surfaces”, Univ. J. Math. Appl., vol. 1, no. 2, pp. 74–79, 2018, doi: 10.32323/ujma.395094.
ISNAD Papadopoulou, Ioanna-Iris - Stamatakis, Stylianos. “On Polar Relative Normalizations of Ruled Surfaces”. Universal Journal of Mathematics and Applications 1/2 (June 2018), 74-79. https://doi.org/10.32323/ujma.395094.
JAMA Papadopoulou I-I, Stamatakis S. On polar relative normalizations of ruled surfaces. Univ. J. Math. Appl. 2018;1:74–79.
MLA Papadopoulou, Ioanna-Iris and Stylianos Stamatakis. “On Polar Relative Normalizations of Ruled Surfaces”. Universal Journal of Mathematics and Applications, vol. 1, no. 2, 2018, pp. 74-79, doi:10.32323/ujma.395094.
Vancouver Papadopoulou I-I, Stamatakis S. On polar relative normalizations of ruled surfaces. Univ. J. Math. Appl. 2018;1(2):74-9.

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