Event

Talk
String action and Generalized Harmonic Maps
Dennis Koh (Potsdam)
8 May 2007, 11:30 – 12:30

In this talk we will introduce the notion of generalized harmonic maps appearing as critical points of a functional that is also considered in string theory. If (M,g) and (N,h) are two closed Riemannian manifolds, the functional is basically given by the energy of a map plus something involving the so-called B-field (Kalb-Ramond field). It turns out that in two special cases the associated Euler-Lagrange equation has interesting interpretations: a) In dim(M)=1 we recover as generalized harmonic maps what is known in physics as magnetic geodesics (Lorentz force). b) If dim(M)<dim(N), restricting the variation of the functional from the class of smooth maps to the class of isometric immersions from M to N has the meaning of prescribing the mean curvature vector field of M in N as a vector field determined by the H-field H=dB (curvature of a gerbe). The idea is to show the existence of generalized harmonic maps with the heat flow method of Eells and Sampson. Short time existence is guaranteed, but long time existence is still a problem.

Related to:

• Dennis Koh