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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 28, Issue 2, Pages 367 - 379 (February 2008)


ON CHARACTERIZATIONS OF SPHERICAL CURVES

Haila Alodan (Saudi Arabia) and Hana Al-Sodais (Saudi Arabia)

Received September 17, 2007

References:



[1] H. Alodan and S. Deshmukh, Compact submanifolds of a Euclidean space, Int. J. Appl. Math. 5(3) (2001), 325-347.

[2] H. Alodan and S. Deshmukh, Spherical submanifolds of a Euclidean space, Quart. J. Math. 53 (2002), 249-256.

[3] W. Boothby, An Introduction to Differential Manifolds and Differential Geometry, Academic Press, New York, 1975.

[4] S. Breuer and D. Gottlieb, Explicit characterization of spherical curves, Proc. Amer. Math. Soc. 27 (1971), 126-127.

[5] B. Y. Chen, Geometry of Submanifolds, Marcel Dekker, Inc., New York, 1973.

[6] S. Deshmukh, Isometric immersion of a compact Riemannian manifold into a Euclidean space, Bull. Austral. Math. Soc. 46(2) (1992), 177-178.

[7] M. P. DoCarmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976.

[8] C. C. Hsiung, A First Course in Differential Geometry, John Wiley & Sons, Inc., U.S.A., 1916.

[9] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry II, Interscience Publ., New York, 1969.

[10] R. S. Millman and G. D. Parker, Elements of Differential Geometry, Prentice Hall Inc., Englewood Cliffs, New Jersey, 1977.

[11] J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math. 88 (1968), 62-105.

[12] Y. C. Wong, On an explicit characterization of spherical curves, Proc. Amer. Math. Soc. 34 (1972), 239-242.

Keywords and phrases: spherical curves, submanifolds, mean curvature.

 


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