Coulomb frames in the normal bundle of surfaces in Euclidean spaces. Topics from differential geometry and geometric analysis of surfaces (Q417407)

This book is dedicated to students and young researchers interested in analysis, partial differential equations and differential geometry. The main goals are: (1) the reinforcement of geometry of surfaces in Euclidean spaces by elements of complex analysis and partial differential equations, (2) a new approach to build orthonormal frames occurring in geometric variational problems. All the material is structured in four chapters: Surface geometry; Elliptic systems; Normal Coulomb frames in \(\mathbb R^4\); Normal Coulomb frames in \(\mathbb R^{n+2}\). These reflect the concerns of the author to produce an original, attractive and intelligent support for students with solid anchor in traditional courses of differential geometry and physics. Threads are complementary to traditional lectures, stimulating curiosity and desire for novelty. The mathematical language is fluent, without mathematical quirks. Carefully selected bibliography is cited in appropriate places.