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• W3109340914 endingPage "112198" @default.
• W3109340914 startingPage "112198" @default.
• W3109340914 abstract "The aim of the paper is to study the geometry of a Riemannian manifold M, with a special structure depending on 3 real parameters, a smooth map φ into a target Riemannian manifold N, and a smooth function f on M itself. We will occasionally let some of the parameters be smooth functions. For a special value of one of them, the structure is obtained by a conformal deformation of a harmonic-Einstein manifold. The setting generalizes various previously studied situations; for instance, Ricci solitons, Ricci harmonic solitons, generalized quasi-Einstein manifolds and so on. One main ingredient of our analysis is the study of certain modified curvature tensors on M, related to the map φ, and to develop a series of results for harmonic-Einstein manifolds that parallel those obtained for Einstein manifolds both some time ago and in the very recent literature. We then turn to locally characterize, via a couple of integrability conditions and mild assumptions on f, the manifold M as a warped product with harmonic-Einstein fibers extending in a very non trivial way a recent result for Ricci solitons. We then consider rigidity and non existence, both in the compact and non-compact cases. This is done via integral formulas and, in the non-compact case, via analytical tools previously introduced by the authors." @default.
• W3109340914 created "2020-12-07" @default.
• W3109340914 creator A5006455486 @default.
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• W3109340914 date "2021-03-01" @default.
• W3109340914 modified "2023-10-16" @default.
• W3109340914 title "On the geometry of Einstein-type structures" @default.
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• W3109340914 doi "https://doi.org/10.1016/j.na.2020.112198" @default.
• W3109340914 hasPublicationYear "2021" @default.
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