Published January 1, 2008 | Version v1
Journal article Open

ON SUBMANIFOLDS SATISFYING CHEN'S EQUALITY IN A REAL SPACE FORM

  • 1. Balikesir Univ, Dept Math, TR-10145 Balikesir, Turkey
  • 2. Univ Lucknow, Dept Math & Astron, Lucknow 226007, Uttar Pradesh, India

Description

Einstein, conformally flat, semisymmetric, and Ricci-semisymmetric submanifolds satisfying Chen's equality in a real space form are studied. We prove that an n-dimensional (n >= 3) submanifold of a real space form (M) over tilde (n+m)(c) satisfying Chen's equality is (i) Einstein if and only if it is a totally geodesic submanifold of constant curvature c; and (ii) conformally flat if and only if inf K=c, where K denotes the sectional curvatures of the submanifold. We also classify semisymmetric and Ricci-semisymmetric submanifolds satisfying Chen's equality in a real space form.

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