Eisenhart's Differential Geometry

Geometry II - Discrete Differential Geometry

Differential Geometry

We discuss intrinsic aspects of Krupka's approach to nite{order variational sequences. We recover in an intrinsic way the second{order varia-tional calculus for aane Lagrangians by means of a natural generalisation of rst{ordertheories. Moreover, we nd an intrinsic expressionfor the Helmholtz morphism using a technique introduced by Koll a r that we have adapted to our context. Introduction The...

Differential Geometry

When studying curves, we studied how the curve twisted and turned in space. We now turn to surfaces, two-dimensional objects in three-dimensional space and examine how the concept of curvature translates to surfaces. In Calculus 3, you have encounter surfaces defined as graphs of real valued functions of two variables z = f(x, y). This function also can take the form x = f(y, z) or y = f(x, z)....

Differential Geometry

In recent years the graph of a foliation, an object which has been known for a long time, cf. 10], has known new interest. In fact there are two groupoids associated with a foliation, the homotopy groupoid and the holonomy groupoid, sometimes called the graph. It serves as a basis for the construction of the C-algebra associated to the foliation. Moreover, the homotopy groupoid of the character...

Differential Geometry