Affiliation:
1. Dipartimento di Matematica “Federigo Enriques” , Universitá degli Studi di Milano , Via Cesare Saldini 50, 20133 , Milano , Italy
Abstract
Abstract
We introduce the notion of rigidity for harmonic-Ricci solitons and provide some characterizations of rigidity, generalizing known results for Ricci solitons. In the complete case we restrict to steady and shrinking gradient solitons, while in the compact case we treat general solitons without further assumptions. We show that the rigidity can be traced back to the vanishing of certain modified curvature tensors that take into account the geometry of a Riemannian manifold equipped with a smooth map φ, called φ-curvature, which is a natural generalization in the setting of harmonic-Ricci solitons of the standard curvature tensor.
Reference31 articles.
1. A. Abolarinwa, Basic structural equations for almost Ricci-harmonic solitons and applications. Differ. Geom. Dyn. Syst. 21 (2019), 1–13. MR3997841 Zbl 1423.53055
2. L. J. Alías, P. Mastrolia, M. Rigoli, Maximum principles and geometric applications. Springer 2016. MR3445380 Zbl 1346.58001
3. A. Anselli, Phi-curvatures, harmonic-Einstein manifolds and Einstein-type structures. PhD thesis, Universitá degli Studi di Milano, 2020.
4. A. Anselli, Bach and Einstein’s equations in presence of a field. Int. J. Geom. Methods. Mod. Phys. 18 (2021), no. 5, 215007. MR4254759
5. A. Anselli, G. Colombo, M. Rigoli, On the geometry of Einstein-type structures. Nonlinear Anal. 204 (2021), 112198. MR4184679 Zbl 7310963
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献