Riemann soliton within the framework of contact geometry. Issue 5 (4th May 2021) - Devaraja, M.N.; Aruna Kumara, H.; Venkatesha, V.
Abstract: In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton ( g, V ) with V as contact vector field on a Sasakian manifold ( M, g ) and in this case we prove that M is either of constant curvature +1 (and V is Killing) or D -homothetically fixed η -Einstein manifold (and V leaves the structure tensor φ invariant). Next, we prove that if a compact K -contact manifold whose metric g is a gradient almost Riemann soliton, then it is Sasakian and isometric to a unit sphere S 2 n +1 . Further, we study H -contact manifold admitting a Riemann soliton ( g, V ) where V is pointwise collinear with ξ .