A Survey on Gradient Ricci Solitons

To solve the Poincaré conjecture on 3-dimensional cases, Richard Hamilton evolved an algorithm called Ricci flow. In Ricci flow, a class of self-similar solutions called gradient solitons. Studing of such kink solution is playing an important role in solving Poincaré conjecture. In 2015, Ovidiu Munteanu and Jiaping Wang shown an algorithm to estimate the Riemann, Ricci curvature and scalar curvature on 4-dimansional gradient solitons in Ricci flow. In this survey, I would introduce some early results in gradient solitons and explore the details in Ovidiu Munteanu and Jiaping Wang’s paper in 4-dimensional shrinking solitons.