Some Aspects of Theoretical Physics Relating to Harmonic Maps

Abstract

Let (M,g) be a compact Riemannian manifold without boundary, and consider an action which, for simplicity, we suppose has the form

$$I\left( \phi \right) = \int\limits_M {L\left( {{j^1}\left( \phi \right)} \right)} \;dx\;, $$

((1.1))

, where Φ is a section of a Riemannian fiber bundle π: E → M, and L: J¹ (E) → ℝ possibly depends on the metric of E.