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The Quarterly Journal of Mathematics Advance Access originally published online on May 24, 2007
The Quarterly Journal of Mathematics 2007 58(3):313-317; doi:10.1093/qmath/ham015
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

REAL HYPERSURFACES IN A EUCLIDEAN COMPLEX SPACE FORM

Sharief Deshmukh{dagger}

Department of Mathematics, College of Science, King Saud University, PO Box 2455, Riyadh-11451, Saudi Arabia

{dagger} E-mail: shariefd{at}ksu.edu.sa

Received 19 June 2006; revised 5 February 2007
  Abstract

Let M be an orientable connected and compact real hypersurface of the complex space form C(n + 1)/2. If the mean curvature {alpha} and the function f = g(A{xi}, {xi}) of hypersurface M satisfy the inequality n2{alpha}2 ≤ (n2 – 1){delta} + f2, where {xi} is the characteristic vector field, A is the shape operator and (n – 1){delta} is the infimum of the Ricci curvatures of hypersurface M, then it is shown that {alpha} is a constant and M is the sphere Sn({alpha}2) in C(n + 1)/2.


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