In this work,we will present a study on the Simons formula and the Simons integral inequality. Both results are fundamental for the study of minimal submanifolds. Our goal is to develop all the fundamental theory necessary to understand and interpret these results. In the first part, we will explore the initial the oryrelated to Riemannian Geometry. We will present a way to derive objects on a manifold and develop a study on the curvature of a Riemannian manifold. We will define what tensors are in a Riemannian manifold, we will explain the concept of isometric immersion sand,seeking to understand its geometry,we will find a (2,1)-tensor called the second fundamental form. In the second part, we will delve deeper into the study of Simons’ formula and inequality. We will demonstrate both results and analyze articles that build on these results.
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