Properties of complete non-compact Yamabe solitons

Abstract

In this article, we first study the local volume estimate of the complete noncompact Yamabe soliton. Then we study the behavior of the potential function of the steady Yamabe soliton with positive Ricci curvature. We also study the scalar curvature decay of steady and expanding Yamabe solitons with Ricci pinching condition.

Triviality results for quasi $k$-Yamabe solitons

“…For instance, if m → ∞, then quasi k-Yamabe solitons reduces to k-Yamabe solitons [2,4,8,23]. Also, since σ 1 = R 2(n−1) , 1-Yamabe solitons naturally correspond to Yamabe solitons [5,6,7,10,11,12,13,15,17,22], and quasi 1-Yamabe solitons correspond to quasi Yamabe solitons studied in [16,25]. When X = ∇f is a gradient vector field, quasi 1-Yamabe gradient solitons correspond to an f -almost Yamabe soliton [27].…”

Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

“…Furthermore, it appears that considering immersions into a sufficiently large family of manifolds, which include spaces with constant sectional curvature, is a handy way to expand the previous studies to a broader class of ambient spaces. Warped product metrics explain a natural metric that includes spaces with constant sectional curvature throughout its range [17][18][19][20][21][22][23][24][25][26].…”

A note on compact CR Yamabe solitons

“…Yamabe soliton has been studied by many authors. See [4,5,9,10,11,16,17,21,22] and the references therein. In particular, we mention the following theorem related to the main result in this paper, which was obtained independently by di Cerbo and Disconzi in [11] and by Hsu in [16]: Suppose (M, θ) is a strictly pseudoconvex CR manifold of real dimension 2n + 1.…”