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Year 2016, Volume: 9 Issue: 1, 0 - 0, 26.06.2016
https://doi.org/10.20854/bujse.258167

Abstract

References

  • Arslan, K., Bulca, B., Bayram, B., Öztürk,G. and Ugail, H. On Spherical Product Surfaces in E³, IEEE Computer Society, International Conference on Cyberworlds, 2009, 132-137.
  • Arslan, K. and Kılıç, B. Product Submanifolds and Their Types, Far East J. Math. Sci.,1998, 6(1), 125-134.
  • Besl, P.J. and Jain, R.C. Invariant Surface Characteristics for 3D Object Recognition in Range Image, Comput. Vis. Graph. Image Process, 1986, 33, 33-80.
  • Bulca, B. and Arslan, K. Mixed Product Surfaces in Euclidean 3-Space E³, Submitted New Trends in Mathematical Sciences.
  • Bulca, B., Arslan, K., Bayram, B.K. and Öztürk, G. Spherical Product Surfaces in E⁴, An. Şt. Univ. Ov. Const., 2012, 20(1), 41-54.
  • Carmo, M.P. Differential Geometry Curves and Surfaces, Englewood Cliffs, New York, Pentice-Hall, 1976.
  • Chen, B.Y. Geometry of Submanifolds, Dekker, New York, 1973.
  • Ganchev,G. and Milousheva, V. On the Theory of Surfaces in the Four dimensional Euclidean space, Kodai Math. J., 2008, 31, 183-198.
  • Gielis, J., Beirinchx, B. and Bastianens,E. Superquadrics with rational and irrational symmetry, Proceedings of the eighth ACM symposium on Solid modeling and applications, 2003, 262-265.
  • Jaklic, A., Leonardis, A. and Solina, F. Segmentation and Recovery of Superquadrics, Kluwer Academic Publishers, 2000.
  • Kuiper, N.H. Minimal total Absolute Curvature for Immersions, Invent. Math.,1970, 10, 209-238.
  • Leonardis, A., Jaklic, A. and Solina, F. Superquadrics for segmenting and modelling data, IEEE Transactions on Pattern Analysis and Machine Intelligence,1997, 19(11), 1289-1295.
  • T. Otsuki, Surfaces in the 4-dimensional Euclidean Space Isometric to a Sphere, Kodai Math. Sem. Rep., 18(1966), 101-115.
  • O' Neill, B. Elementary Differential Geometry, Academic Press, USA, 1997.
  • Pentland, A.P. Percettual Organization and the Representation of Natural Form, Artificial Intelligence, 28(1986), 293-331.

MIXED PRODUCT SURFACES IN E^4

Year 2016, Volume: 9 Issue: 1, 0 - 0, 26.06.2016
https://doi.org/10.20854/bujse.258167

Abstract

In the present study we define a new kind of product surfaces namely mixed products which are product of two space curves in 4-dimensional Euclidean space . We investigate the Gaussian curvature, Gaussian torsion and mean curvature of these kind of surfaces. We obtain some original results of mixed product surfaces in . Further, we give some examples of these kind of surfaces.

References

  • Arslan, K., Bulca, B., Bayram, B., Öztürk,G. and Ugail, H. On Spherical Product Surfaces in E³, IEEE Computer Society, International Conference on Cyberworlds, 2009, 132-137.
  • Arslan, K. and Kılıç, B. Product Submanifolds and Their Types, Far East J. Math. Sci.,1998, 6(1), 125-134.
  • Besl, P.J. and Jain, R.C. Invariant Surface Characteristics for 3D Object Recognition in Range Image, Comput. Vis. Graph. Image Process, 1986, 33, 33-80.
  • Bulca, B. and Arslan, K. Mixed Product Surfaces in Euclidean 3-Space E³, Submitted New Trends in Mathematical Sciences.
  • Bulca, B., Arslan, K., Bayram, B.K. and Öztürk, G. Spherical Product Surfaces in E⁴, An. Şt. Univ. Ov. Const., 2012, 20(1), 41-54.
  • Carmo, M.P. Differential Geometry Curves and Surfaces, Englewood Cliffs, New York, Pentice-Hall, 1976.
  • Chen, B.Y. Geometry of Submanifolds, Dekker, New York, 1973.
  • Ganchev,G. and Milousheva, V. On the Theory of Surfaces in the Four dimensional Euclidean space, Kodai Math. J., 2008, 31, 183-198.
  • Gielis, J., Beirinchx, B. and Bastianens,E. Superquadrics with rational and irrational symmetry, Proceedings of the eighth ACM symposium on Solid modeling and applications, 2003, 262-265.
  • Jaklic, A., Leonardis, A. and Solina, F. Segmentation and Recovery of Superquadrics, Kluwer Academic Publishers, 2000.
  • Kuiper, N.H. Minimal total Absolute Curvature for Immersions, Invent. Math.,1970, 10, 209-238.
  • Leonardis, A., Jaklic, A. and Solina, F. Superquadrics for segmenting and modelling data, IEEE Transactions on Pattern Analysis and Machine Intelligence,1997, 19(11), 1289-1295.
  • T. Otsuki, Surfaces in the 4-dimensional Euclidean Space Isometric to a Sphere, Kodai Math. Sem. Rep., 18(1966), 101-115.
  • O' Neill, B. Elementary Differential Geometry, Academic Press, USA, 1997.
  • Pentland, A.P. Percettual Organization and the Representation of Natural Form, Artificial Intelligence, 28(1986), 293-331.
There are 15 citations in total.

Details

Journal Section Articles
Authors

Betül Bulca

Kadri Arslan

Publication Date June 26, 2016
Published in Issue Year 2016 Volume: 9 Issue: 1

Cite

APA Bulca, B., & Arslan, K. (2016). MIXED PRODUCT SURFACES IN E^4. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 9(1). https://doi.org/10.20854/bujse.258167
AMA Bulca B, Arslan K. MIXED PRODUCT SURFACES IN E^4. BUJSE. June 2016;9(1). doi:10.20854/bujse.258167
Chicago Bulca, Betül, and Kadri Arslan. “MIXED PRODUCT SURFACES IN E^4”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 9, no. 1 (June 2016). https://doi.org/10.20854/bujse.258167.
EndNote Bulca B, Arslan K (June 1, 2016) MIXED PRODUCT SURFACES IN E^4. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 9 1
IEEE B. Bulca and K. Arslan, “MIXED PRODUCT SURFACES IN E^4”, BUJSE, vol. 9, no. 1, 2016, doi: 10.20854/bujse.258167.
ISNAD Bulca, Betül - Arslan, Kadri. “MIXED PRODUCT SURFACES IN E^4”. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 9/1 (June 2016). https://doi.org/10.20854/bujse.258167.
JAMA Bulca B, Arslan K. MIXED PRODUCT SURFACES IN E^4. BUJSE. 2016;9. doi:10.20854/bujse.258167.
MLA Bulca, Betül and Kadri Arslan. “MIXED PRODUCT SURFACES IN E^4”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 9, no. 1, 2016, doi:10.20854/bujse.258167.
Vancouver Bulca B, Arslan K. MIXED PRODUCT SURFACES IN E^4. BUJSE. 2016;9(1).