AM  Vol.6 No.8 , July 2015
Studying Scalar Curvature of Two Dimensional Kinematic Surfaces Obtained by Using Similarity Kinematic of a Deltoid
Abstract: We consider a similarity kinematic of a deltoid by studying locally the scalar curvature for the corresponding two dimensional kinematic surfaces in the Euclidean space . We prove that there is no two dimensional kinematic surfaces with scalar curvature K is non-zero constant. We describe the equations that govern such the surfaces.
Cite this paper: Solouma, E. , Wageeda, M. , Gouda, Y. and Bary, M. (2015) Studying Scalar Curvature of Two Dimensional Kinematic Surfaces Obtained by Using Similarity Kinematic of a Deltoid. Applied Mathematics, 6, 1353-1361. doi: 10.4236/am.2015.68128.

[1]   Connor, O.J. and Robertson, E. (2006) Biography: Euler and Steiner.

[2]   Barros, M. (1997) General Helices and a Theorem of Lancret. Proceedings of the American Mathematical Society, 125, 1503-1509.

[3]   Abdel-All, N.H. and Hamdoon, F.M. (2004) Cyclic Surfaces in E5 Generated by Equiform Motions. Journal of Geometry, 79, 1-11.

[4]   Gordon, V.O. and Sement Sov, M.A. (1980) A Course in Descriptive Geometry. Mir Publishers, Moscow.

[5]   Solouma, E.M. (2015) Three Dimensional Surfaces Foliated by an Equiform Motion of Pseudohyperbolic Surfaces in . JP Journal of Geometry and Topology, 0972-451x.

[6]   Solouma, E.M. (2012) Local Study of Scalar Curvature of Two-Dimensional Surfaces Obtained by the Motion of Circle. Journal of Applied Mathematics and Computation, 219, 3385-3394.

[7]   Solouma, E.M., et al. (2007) Three Dimensional Surfaces Foliated by Two Dimensional Spheres. Journal of Egyptian Mathematical Society, 1, 101-110.

[8]   Bottema, O. and Roth, B. (1990) Theoretical Kinematic. Dover Publications Inc., New York.

[9]   Farin, G., Hoschek, J. and Kim, M. (2002) The Handbook of Computer Aided Geometric Design. North-Holland, Amsterdam.

[10]   Castro, I. and Urbano, F. (1999) On a Minimal Lagrangian Submanifold of Cn Foliated by Spheres. Michigan Mathematical Journal, 46, 71-82.

[11]   Jagy, W. (1998) Sphere Foliated Constant Mean Curvature Submanifolds. Rocky Mountain Journal of Mathematics, 28, 983-1015.

[12]   López, R. (2002) Cyclic Hypersurfaces of Constant Curvature. Advances Studies in Mathematics, 34, 185-199.

[13]   Park, S.H. (2002) Sphere Foliated Minimal and Constant Mean Curvature Hypersurfaces in Space Forms Lorentz- Minkowski Space. Rocky Mountain Journal of Mathematics, 32, 1019-1044.

[14]   Kreyszig, E. (1975) Introduction to Differential Geometry and Riemannian Geometry. University of Toronto Press, Canada.

[15]   Do Carmo, M. (1976) Differential Geometry of Curves and Surfaces. Prentice-Hall Inc., Englewood Cliffs.