Local Study of Scalar Curvature of Cyclic Surfaces Obtained by Homothetic Motion of Lorentzian Circle

Affiliation(s)

^{1}
Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt.

^{2}
Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt.

ABSTRACT

In this paper we consider the homothetic motion of Lorentzian circle by studying the scalar curvature for the corresponding cyclic surface locally. We prove that if the scalar curvature is constant, then . We describe the equations that govern such surfaces.

In this paper we consider the homothetic motion of Lorentzian circle by studying the scalar curvature for the corresponding cyclic surface locally. We prove that if the scalar curvature is constant, then . We describe the equations that govern such surfaces.

Cite this paper

Wageeda, M. and Solouma, E. (2015) Local Study of Scalar Curvature of Cyclic Surfaces Obtained by Homothetic Motion of Lorentzian Circle.*Applied Mathematics*, **6**, 1344-1352. doi: 10.4236/am.2015.68127.

Wageeda, M. and Solouma, E. (2015) Local Study of Scalar Curvature of Cyclic Surfaces Obtained by Homothetic Motion of Lorentzian Circle.

References

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

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

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

http://dx.doi.org/10.1216/rmjm/1181071750

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

[5] Odehnal, B., Pottmann, H. and Wallner, J. (2006) Equiform Kinematics and the Geometry of Line Elements. Beiträge zur Algebra und Geometrie, 47, 567-582.

[6] Pottmann, H. and Wallner, J. (2001) Computational Line Geometry. Springer Heidelberg Dordrecht, London, New York.

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

http://dx.doi.org/10.1007/s00022-003-1682-2

[8] Solouma, E.M. (2015) Three Dimensional Surfaces Foliated by an Equiform Motion of Pseudohyperbolic Surfaces in . JP Journal of Geometry and Topology, Accepted (To appear).

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

http://dx.doi.org/10.1016/j.amc.2012.09.066

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

[11] O’Neill, B. (1983) Semi-Riemannian Geometry with Application to Relativity. Academic Press, New York and London.

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

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

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

http://dx.doi.org/10.1216/rmjm/1181071750

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

[5] Odehnal, B., Pottmann, H. and Wallner, J. (2006) Equiform Kinematics and the Geometry of Line Elements. Beiträge zur Algebra und Geometrie, 47, 567-582.

[6] Pottmann, H. and Wallner, J. (2001) Computational Line Geometry. Springer Heidelberg Dordrecht, London, New York.

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

http://dx.doi.org/10.1007/s00022-003-1682-2

[8] Solouma, E.M. (2015) Three Dimensional Surfaces Foliated by an Equiform Motion of Pseudohyperbolic Surfaces in . JP Journal of Geometry and Topology, Accepted (To appear).

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

http://dx.doi.org/10.1016/j.amc.2012.09.066

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

[11] O’Neill, B. (1983) Semi-Riemannian Geometry with Application to Relativity. Academic Press, New York and London.