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

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 28, Issue 3, Pages 657 - 666 (March 2008)


SUBMANIFOLDS OF EINSTEIN MANIFOLDS

Falleh R. Al-solamy (Saudi Arabia)

Received November 15, 2007

References:



[1] A. L. Besse, Einstein Manifolds, Springer-Verlag, 1987.

[2] B. Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, World Scientific, 1983.

[3] B. Y. Chen and O. J. Garay, Constant mean curvature hypersurfaces with constant
d-invariant, Int. J. Math. Math. Sci. 67 (2003), 4205-4216.

[4] C. Chen, H. Sun and L. Tang, On translation hypersurfaces with constant mean curvature in (n+1)-dimensional spaces, J. Beijing Inst. Technol. 12 (2003), 322-325.

[5] S. Deshmukh and M. A. Al-Gwaiz, Compact hypersurfaces in even-dimensional Euclidean space and in the sphere, Quart. J. Math. Oxford Ser. (2) 45 (1994), 151-157.

[6] S. Kobayashi and K. Nomizu, Foundations in Differential Geometry, Wiley-Interscience, New York, 1969.

[7] R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms, Tight and Taut Submanifolds (Berkeley, CA, 1994), 233-305, Math. Sci. Res. Inst. Publ., 32, Cambridge Univ. Press, Cambridge, 1997.

[8] K. Nomizu and B. Smyth, A formula of Simon’s type and hypersurfaces with constant mean curvature, J. Differential Geom. 3 (1969), 367-377.

[9] K. Nomizu and B. Smyth, On the Gauss mapping for hypersurfaces of constant mean curvature in the sphere, Comment. Math. Helv. 44 (1969), 484-490.

[10] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, London, 1983.

Keywords and phrases: submanifolds of an Einstein manifold, mixed sectional curvature, Ricci curvature, mean curvature.

 


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