Israel Journal of Mathematics

, Volume 100, Issue 1, pp 163–169 | Cite as

Einstein, conformally flat and semi-symmetric submanifolds satisfying chen’s equality



In a recent paper, B. Y. Chen proved a basic inequality between the intrinsic scalar invariants infK andτ ofM n , and the extrinsic scalar invariant |H|, being the length of the mean curvature vector fieldH ofM n in\(\mathbb{E}^m \). In the present paper we classify the submanifoldsM n of\(\mathbb{E}^m \) for which the basic inequality actually is an equality, under the additional assumption thatM n satisfies some of the most primitive Riemannian curvature conditions, such as to be Einstein, conformally flat or semi-symmetric.


Sectional Curvature Curvature Tensor Complex Space Form Basic Inequality Real Submanifolds 


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Copyright information

© Hebrew University 1997

Authors and Affiliations

  1. 1.Departement WiskundeKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Department of MathematicsUniversity Svetozar Markovic Radoja DomanovicaKragujevacYugoslavia
  3. 3.Departement WiskundeKatholieke Universiteit LeuvenLeuvenBelgium
  4. 4.Group of Exact SciencesKatholieke Universiteit BrusselBrusselBelgium

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