Complete gradient Einstein-type Sasakian manifolds with $\alpha=0$

Shun Maeta

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arXiv · 2510.12441

Complete gradient Einstein-type Sasakian manifolds with $\alpha=0$

Shun Maeta

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Abstract

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 $\alpha, \beta, \mu$ and $\rho$. In this paper, we show that when $\alpha = 0$, 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.

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Shun Maeta. 2025-10-14. Complete gradient Einstein-type Sasakian manifolds with $\alpha=0$. https://arxiv.org/abs/2510.12441

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