Almost Schouten solitons and contact geometry

Changhwa Woo, Arpan Sardar, Uday Chand De

Abstract


The current article is about almost Schouten solitons and gradient Schouten solitons on contact geometry. At first, we demonstrate that if a compact $K$-contact manifold admits an almost Schouten soliton, then the soliton is shrinking and the manifold is an Einstein manifold. Moreover, we show that if a $K$-contact manifold admits a gradient Schouten soliton, then the manifold becomes an Einstein manifold. Next, we investigate almost Schouten solitons and gradient Schouten solitons on $(k,\mu)$-contact manifolds. Finally, we show that if a complete $H$-contact manifold $M^{2n+1}$ satisfying certain restriction on the scalar curvature and the soliton function admits an almost Schouten soliton whose potential vector field $V$ is collinear with $\zeta$, then $M^{2n+1}$ is compact Einstein and Sasakian.

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