Differential-Geometric Methods in the Calculus of Variations

Abstract

The so-called metric theories, based on the concept of a metric, occupy an important place in differential geometry. Most of all the giving of these metrics can be looked upon as the giving of functionals of various variational problems on appropriate spaces, which leads to the interconnection of differential geometry and the calculus of variations. From this connection differential geometry obtains the possibility of the development of new theories and of the posing of new problems, while the application of intrinsic geometrical methods in the calculus of variations, in addition to clarifying the essence of the results by means of a geometrical interpretation, can prove to be useful for the creation of new research methods.