Conformal Immersions, and Gravity
نویسندگان
چکیده
Basic quantities related to 2-D gravity, such as Polyakov extrinsic action, Nambu-Goto action, geometrical action, and Euler characteristic are studied using generalized Weierstrass-Enneper (GWE) inducing of surfaces in R3. Connection of the GWE inducing with conformal immersion is made and various aspects of the theory are shown to be invariant under the modified VeselovNovikov hierarchy of flows. The geometry of h √ g = 1 surfaces (h ∼ mean curvature) is shown to be connected with the dynamics of infinite and finite dimensional integrable systems. Connections to Liouville-Beltrami gravity are indicated.
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