Differential Geometry Tu Loring W.
Differential Geometry Tu Loring W. This text presents a graduate-level introduction to differential geometry for mathematics and physics students. Along the way we encounter some of the high points…
Specifikacia Differential Geometry Tu Loring W.
Differential Geometry Tu Loring W.
This text presents a graduate-level introduction to differential geometry for mathematics and physics students. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss-Bonnet theorem. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern-Weil theory of characteristic classes on a principal bundle.
Initially, the prerequisites for the reader include a passing familiarity with manifolds. Exercises throughout the book test the reader's understanding of the material and sometimes illustrate extensions of the theory. After the first chapter, it becomes necessary to understand and manipulate differential forms.
A knowledge of de Rham cohomology is required for the last third of the text.Prerequisite material is contained in
Differential Geometry
Functional Differential Geometry