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Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces

Year 2017, Volume: 10 Issue: 1, 86 - 95, 30.04.2017
https://doi.org/10.36890/iejg.584447

Abstract

References

  • [1] Cambie, S., Goemans, W. and Van den Bussche, I., Rectifying curves in the n-dimensional Euclidean space. Turkish J. Math., 40 (2016), no.1, 210-223.
  • [2] Chen, B.-Y., Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean space, J. Geom., 74 (2002), 61-77.
  • [3] Chen, B.-Y., When does the position vector of a space curve always lie in its rectifying plane? Amer. Math. Monthly, 110 (2003), no. 2, 147–152.
  • [4] Chen, B.-Y., Constant-ratio space-like submanifolds in pseudo-Euclidean space. Houston J. Math., 29 (2003), no. 2, 281-294. [5] Chen, B.-Y., Riemannian geometry, δ-invariants and applications. World Scientific, Hackensack, NJ, 2011.
  • [6] Chen, B.-Y., Differential geometry of rectifying submanifolds. Int. Electron. J. Geom., 9 (2016), no. 2, 1-8.
  • [7] Chen, B.-Y., Addendum to : Differential geometry of rectifying submanifolds. Int. Electron. J. Geom., 10 (2017), no. 1, 81-82.
  • [8] Chen, B.-Y., Differential geometry of warped product manifolds and submanifolds. World Scientific, Hackensack, NJ, 2017.
  • [9] Chen, B.-Y., Rectifying curves and geodesics on a cone in the Euclidean 3-space. Tamkang J. Math., 48 (2017) (to appear).
  • [10] Chen, B.-Y. and Dillen, F., Rectifying curves as centrodes and extremal curves. Bull. Inst. Math. Acad. Sinica 33 (2005), no. 2, 77-90.
  • [11] Kim, D.-S., Chung, H.-S. and Cho, K.-H., Space curves satisfying τ/κ = as + b. Honam Math. J., 15 (1993), 1-9.
  • [12] Hiepko, S., Eine innere Kennzeichnung der verzerrten Produkte. Math. Ann. , 241 (1979), no. 3, 209-215.
  • [13] Ilarslan, K., Nesovic, E. and Petrovic-Torgasev, M., Some characterizations of rectifying curves in the Minkowski 3-space. Novi Sad J. Math., 33 (2003), no. 2, 23-32.
  • [14] Ilarslan, K. and Nesovic, E., On rectifying curves as centrodes and extremal curves in the Minkowski 3-space. Novi Sad J. Math. 37 (2007), no. 1, 53-64.
  • [15] Ilarslan, K. and Nesovic, E., Some relations between normal and rectifying curves in Minkowski space-time. Int. Electron. J. Geom. 7 (2014), no. 1, 26-35.
  • [16] O’Neill, B., Semi-Riemannian geometry with applications to relativity. Academic Press, New York, 1983.
Year 2017, Volume: 10 Issue: 1, 86 - 95, 30.04.2017
https://doi.org/10.36890/iejg.584447

Abstract

References

  • [1] Cambie, S., Goemans, W. and Van den Bussche, I., Rectifying curves in the n-dimensional Euclidean space. Turkish J. Math., 40 (2016), no.1, 210-223.
  • [2] Chen, B.-Y., Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean space, J. Geom., 74 (2002), 61-77.
  • [3] Chen, B.-Y., When does the position vector of a space curve always lie in its rectifying plane? Amer. Math. Monthly, 110 (2003), no. 2, 147–152.
  • [4] Chen, B.-Y., Constant-ratio space-like submanifolds in pseudo-Euclidean space. Houston J. Math., 29 (2003), no. 2, 281-294. [5] Chen, B.-Y., Riemannian geometry, δ-invariants and applications. World Scientific, Hackensack, NJ, 2011.
  • [6] Chen, B.-Y., Differential geometry of rectifying submanifolds. Int. Electron. J. Geom., 9 (2016), no. 2, 1-8.
  • [7] Chen, B.-Y., Addendum to : Differential geometry of rectifying submanifolds. Int. Electron. J. Geom., 10 (2017), no. 1, 81-82.
  • [8] Chen, B.-Y., Differential geometry of warped product manifolds and submanifolds. World Scientific, Hackensack, NJ, 2017.
  • [9] Chen, B.-Y., Rectifying curves and geodesics on a cone in the Euclidean 3-space. Tamkang J. Math., 48 (2017) (to appear).
  • [10] Chen, B.-Y. and Dillen, F., Rectifying curves as centrodes and extremal curves. Bull. Inst. Math. Acad. Sinica 33 (2005), no. 2, 77-90.
  • [11] Kim, D.-S., Chung, H.-S. and Cho, K.-H., Space curves satisfying τ/κ = as + b. Honam Math. J., 15 (1993), 1-9.
  • [12] Hiepko, S., Eine innere Kennzeichnung der verzerrten Produkte. Math. Ann. , 241 (1979), no. 3, 209-215.
  • [13] Ilarslan, K., Nesovic, E. and Petrovic-Torgasev, M., Some characterizations of rectifying curves in the Minkowski 3-space. Novi Sad J. Math., 33 (2003), no. 2, 23-32.
  • [14] Ilarslan, K. and Nesovic, E., On rectifying curves as centrodes and extremal curves in the Minkowski 3-space. Novi Sad J. Math. 37 (2007), no. 1, 53-64.
  • [15] Ilarslan, K. and Nesovic, E., Some relations between normal and rectifying curves in Minkowski space-time. Int. Electron. J. Geom. 7 (2014), no. 1, 26-35.
  • [16] O’Neill, B., Semi-Riemannian geometry with applications to relativity. Academic Press, New York, 1983.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Bang-yen Chen

Yun Myung Oh This is me

Publication Date April 30, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

APA Chen, B.-y., & Oh, Y. M. (2017). Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces. International Electronic Journal of Geometry, 10(1), 86-95. https://doi.org/10.36890/iejg.584447
AMA Chen By, Oh YM. Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces. Int. Electron. J. Geom. April 2017;10(1):86-95. doi:10.36890/iejg.584447
Chicago Chen, Bang-yen, and Yun Myung Oh. “Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces”. International Electronic Journal of Geometry 10, no. 1 (April 2017): 86-95. https://doi.org/10.36890/iejg.584447.
EndNote Chen B-y, Oh YM (April 1, 2017) Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces. International Electronic Journal of Geometry 10 1 86–95.
IEEE B.-y. Chen and Y. M. Oh, “Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces”, Int. Electron. J. Geom., vol. 10, no. 1, pp. 86–95, 2017, doi: 10.36890/iejg.584447.
ISNAD Chen, Bang-yen - Oh, Yun Myung. “Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces”. International Electronic Journal of Geometry 10/1 (April 2017), 86-95. https://doi.org/10.36890/iejg.584447.
JAMA Chen B-y, Oh YM. Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces. Int. Electron. J. Geom. 2017;10:86–95.
MLA Chen, Bang-yen and Yun Myung Oh. “Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces”. International Electronic Journal of Geometry, vol. 10, no. 1, 2017, pp. 86-95, doi:10.36890/iejg.584447.
Vancouver Chen B-y, Oh YM. Classification of Rectifying Space-Like Submanifolds in Pseudo-Euclidean Spaces. Int. Electron. J. Geom. 2017;10(1):86-95.