MIXED PRODUCT SURFACES IN E^4

Öz

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.

Anahtar Kelimeler

• Spherical Product,Mixed Product; Gaussian torsion; Mean curvature

Kaynakça

1. 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.
2. Arslan, K. and Kılıç, B. Product Submanifolds and Their Types, Far East J. Math. Sci.,1998, 6(1), 125-134.
3. 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.
4. Bulca, B. and Arslan, K. Mixed Product Surfaces in Euclidean 3-Space E³, Submitted New Trends in Mathematical Sciences.
5. 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.
6. Carmo, M.P. Differential Geometry Curves and Surfaces, Englewood Cliffs, New York, Pentice-Hall, 1976.
7. Chen, B.Y. Geometry of Submanifolds, Dekker, New York, 1973.
8. Ganchev,G. and Milousheva, V. On the Theory of Surfaces in the Four dimensional Euclidean space, Kodai Math. J., 2008, 31, 183-198.

9. 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.
10. Jaklic, A., Leonardis, A. and Solina, F. Segmentation and Recovery of Superquadrics, Kluwer Academic Publishers, 2000.
11. Kuiper, N.H. Minimal total Absolute Curvature for Immersions, Invent. Math.,1970, 10, 209-238.
12. 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.
13. T. Otsuki, Surfaces in the 4-dimensional Euclidean Space Isometric to a Sphere, Kodai Math. Sem. Rep., 18(1966), 101-115.
14. O' Neill, B. Elementary Differential Geometry, Academic Press, USA, 1997.
15. Pentland, A.P. Percettual Organization and the Representation of Natural Form, Artificial Intelligence, 28(1986), 293-331.