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QUASI-EINSTEIN CONTACT METRIC MANIFOLDS

Part of: Global differential geometry

Published online by Cambridge University Press:  18 December 2014

AMALENDU GHOSH
AMALENDU GHOSH*
Affiliation:
Department of Mathematics, Chandernagore College, Chandannagar, 712 136, W.B.India e-mail: [email protected]
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Abstract

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We consider quasi-Einstein metrics in the framework of contact metric manifolds and prove some rigidity results. First, we show that any quasi-Einstein Sasakian metric is Einstein. Next, we prove that any complete K-contact manifold with quasi-Einstein metric is compact Einstein and Sasakian. To this end, we extend these results for (κ, μ)-spaces.

MSC classification

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 3 , September 2015 , pp. 569 - 577
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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