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http://dx.doi.org/10.4134/CKMS.c190247

GRADIENT EINSTEIN-TYPE CONTACT METRIC MANIFOLDS  

Kumara, Huchchappa Aruna (Department of Mathematics Kuvempu University)
Venkatesha, Venkatesha (Department of Mathematics Kuvempu University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 639-651 More about this Journal
Abstract
Consider a gradient Einstein-type metric in the setting of K-contact manifolds and (κ, µ)-contact manifolds. First, it is proved that, if a complete K-contact manifold admits a gradient Einstein-type metric, then M is compact, Einstein, Sasakian and isometric to the unit sphere 𝕊2n+1. Next, it is proved that, if a non-Sasakian (κ, µ)-contact manifolds admits a gradient Einstein-type metric, then it is flat in dimension 3, and for higher dimension, M is locally isometric to the product of a Euclidean space 𝔼n+1 and a sphere 𝕊n(4) of constant curvature +4.
Keywords
Einstein-type manifolds; K-contact manifolds; Sasakian manifold; (${\kappa},{\mu}$)-contact manifold; Einstein manifold;
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