https://neckpinch.com/authors/shun-maeta/New arXiv papers by Shun Maeta, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2510.12441arxiv:2510.12441Tue, 14 Oct 2025 00:00:00 GMTShun Maeta — Catino, Mastrolia, Monticelli, and Rigoli have launched an ambitious program to study known geometric solitons from a unified perspective, which they term Einstein-type manifolds. This framework allows one to treat Ricci solitons, Yamabe solitons, and all of their generalizations simultaneously. Einstein-type manifolds are characterized by four constants α, β, μ and ρ. In this paper, we show that when α= 0, complete gradient Einstein-type Sasakian manifolds are trivial or isometric to the unit sphere. As a consequence, many geometric solitons on Sasakian manifolds turn out to be trivial or isometric to the unit sphere.Ricci solitonsAlmost & η-Ricci solitonsSasakian & contact geometry https://arxiv.org/abs/2503.19596arxiv:2503.19596Tue, 25 Mar 2025 00:00:00 GMTShun Maeta — Thanks to the ambitious project initiated by Catino, Mastrolia, Monticelli and Rigoli, which aims to provide a unified viewpoint for various geometric solitons, many classes, including Ricci solitons, Yamabe solitons, k-Yamabe solitons, quasi-Yamabe solitons, and conformal solitons, can now be studied under a unified framework known as Einstein-type manifolds. Einstein-type manifolds are characterized by four constants, denoted by α, β, μ and ρ. In this paper, we completely classify all non-trivial, complete gradient Einstein-type Kähler manifolds with α= 0. As a corollary, rotational symmetry for many classes is obtained. In particular, we show that any non-trivial complete gradient quasi-Yamabe soliton on Kähler manifolds is rotationally symmetric.Ricci solitonsAlmost & η-Ricci solitonsKähler geometryRotational symmetry & warped products https://arxiv.org/abs/2208.09162arxiv:2208.09162Fri, 19 Aug 2022 00:00:00 GMTShun Maeta — We consider the broadest concept of the gradient Yamabe soliton, the conformal gradient soliton. In this paper, we elucidate the structure of complete gradient conformal solitons under some assumption, and provide some applications to gradient Yamabe solitons. These results enhance the understanding gained from previous research. Furthermore, we give an affirmative partial answer to the Yamabe soliton version of Perelman's conjecture.Ricci solitonsAlmost & η-Ricci solitons https://arxiv.org/abs/2107.05487arxiv:2107.05487Mon, 12 Jul 2021 00:00:00 GMTShun Maeta — We study complete conformal gradient solitons, a class containing gradient Yamabe solitons and many generalized Yamabe-type structures, including gradient almost Yamabe, gradient k-Yamabe, and gradient h-almost Yamabe solitons, and, after a change of the potential function, gradient Einstein-type manifolds with α=0 and β≠0 (in particular, quasi-Yamabe solitons). In this paper, we classify complete nontrivial locally conformally flat conformal gradient solitons. This result contributes to an analogue of Perelman's conjecture for Yamabe-type solitons. Moreover, we show that under nonnegative scalar curvature, every nonflat soliton is rotationally symmetric. We also obtain classifications assuming the Cotton or Cao-Chen tensor vanishes.Ricci solitonsAlmost & η-Ricci solitonsScalar curvatureRotational symmetry & warped products