Sobre estruturas gradiente Einstein-type produto torcido
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2022-04-13
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Universidade Federal de Goiás
Resumo
In this work, we study gradient Einstein-type structures immersed in a warped
product space of an interval I and a Riemannian manifold M, with a potential function h given by the height function. First, we obtained the necessary conditions for an Einstein-type gradient structure immersed in a warped product to be minimal, totally umbilic or totally geodesic. In addition, we provide triviality results for the potential function h. Next, we characterize the rotational hypersurfaces having a gradient Einstein-type structure in warped product, where the fiber is a space form. We also study particular cases of gradient Einstein-type structures in warped product spaces, namely, gradient Ricci-harmonic solitons (GRHS). In this case, we prove triviality results for the potential and warped functions when they reach a maximum or minimum. Finally, we provide a family non-enumerable of non-trivial geodesically complete examples of GRHS considering the base and fiber of a warped product conformal to a semi-Euclidean space invariant under the action of a translation group of codimension one.
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Citação
BATISTA, E. D. Sobre estruturas gradiente Einstein-type produto torcido. 2022. 95 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.