The Geometry of Vector Fields

Presenting a classical approach to the foundations and development of the geometry of vector fields, this volume describes vector fields in three-dimensional Euclidean space, three orthogonal systems, and applications in mechanics. Other topics, including vector fields, Pfaff forms and systems in n-dimensional space, foliations and Godbillon-Vey invariant, are also considered. There is much interest in the study of geometrical objects in n-dimensional Euclidean space, and this volume provides a useful and comprehensive presentation. A specialist in classical differential geometry, Aminov (Ukrainian Academy of Sciences, Kharkov) presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space and triply-orthogonal systems. He also discusses Pfaffian forms and systems in n-dimensional space, foliations and their Godbillon-Vey invariant, and applications in mechanics. Annotation copyrighted by Book News, Inc., Portland, OR Presenting a classical approach to the foundations and development of the geometry of vector fields, this volume tackles three orthogonal systems and applications in mechanics. Other topics, including vector fields, Pfaff forms and systems in n-dimensional space, foliations and Godbillon-Vey invariant, are also considered. Let us consider a family of surfaces defined in some domain G of three-dimensional Euclidean space E3.