Geodesic
QUASI-EINSTEIN CONTACT METRIC MANIFOLDS
Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 569-577

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DOI

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. 
GHOSH, AMALENDU. QUASI-EINSTEIN CONTACT METRIC MANIFOLDS. Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 569-577. doi: 10.1017/S0017089514000494
@article{10_1017_S0017089514000494,
     author = {GHOSH, AMALENDU},
     title = {QUASI-EINSTEIN {CONTACT} {METRIC} {MANIFOLDS}},
     journal = {Glasgow mathematical journal},
     pages = {569--577},
     year = {2015},
     volume = {57},
     number = {3},
     doi = {10.1017/S0017089514000494},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000494/}
}
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