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A Riemannian invariant and its applications to Einstein manifolds

Published online by Cambridge University Press:  17 April 2009

Bang-Yen Chen
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824–1027, United States of America, e-mail: bychen@math.msu.edu
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Extract

We introduce a Riemannian invariant and establish general optimal inequalities involving the invariants and the squared mean curvature for Einstein manifolds isometrically immersed in real space forms. We show that these inequalities do not hold for arbitrary submanifolds in real space forms in general. We also provide some immediate applications of the inequalities.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Chen, B.Y., Geometry of submanifolds (M. Dekker, New York, 1973).Google Scholar
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