The Theory of Submanifolds emerged as a natural generalization of the classical study of curves and surfaces of three-dimensional Euclidean space through the methods of differential calculus. In the last century, this theory has become a vast sub-area of Differential Geometry with numerous correlated lines of research and a variety of techniques that allow obtaining many deep research results, both local and global. A significant part of these techniques originated in Geometric Analysis, whose scope includes the use of geometric methods in the study of partial differential equations (PDE’s) and, conversely, the application of the theory of PDE’s to Differential Geometry. In the last decades, an important school of geometers from Brazil, Spain, Colombia and Mexico has been working intensively on the theory of submanifolds (surfaces, hypersurfaces, isometric immersions) and on Geometric Analysis, initiated by pioneers such as Manfredo do Carmo, Greg Galloway, Santiago López de Medrano and Antonio Martínez Naveira.
In this research school, the students will have contact with geometers, some of them oriented by the pioneers cited above. The introductory courses of the first week will teach the techniques of classical geometry of curves and surfaces in Euclidean and/or Lorentzian spaces, covering intrinsic (Gaussian curvature) and extrinsic (mean curvature) invariants from a global point of view.
Scientific program is available on the local website of the School: https://naturales.ues.edu.sv/ecimpasv2024/
Official language of the school: Spanish