2023-06-052023-06-052023-05-12NOVAIS, R. M. Fluxo de curvatura média e hipersuperfícies Tipo-T-Einstein. 2023. 105 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2023.http://repositorio.bc.ufg.br/tede/handle/tede/12881We present an analysis of the self-similar solutions of Mean Curvature Flow (MCF) by ruled and revolution surfaces in $\mathbb{R}^{3}$. We prove that homothetic helicoidal motion solutions whose initial condition is a non-cylindrical ruled surface must be trivial. When the initial condition is a surface of revolution, we characterize the solutions in terms of the curvature of the generatrix curve. We characterize the curve shortening flow (CSF) soliton solutions on the torus of revolution $\mathbb{T}^{2}\subset\mathbb{R}^3$. We show that the solutions must be asymptotic to the equators of the torus. Furthermore, we generalize this result to surfaces of revolution in $\mathbb{R}^3$. Finally, we prove that a class of Einstein-type hypersurfaces in $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$ are rotational or totally umbilical hypersurfaces.Attribution-NonCommercial-NoDerivatives 4.0 InternationalFluxo de curvatura médiaFluxo redutor de curvasAuto-similarSolitonTipo-EinsteinHipersuperfícies de rotaçãoMean curvature flowCurve shortening flowSelf-similarEinstein-typeRotation hypersurfaceCIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIATese