Metric-Independent Measures for Supersymmetric Extended Object Theories on Curved Backgrounds

For Green-Schwarz superstring sigma-model on curved backgrounds, we introduce a non-metric measure $\Phi \equiv \epsilon^{i j} \epsilon^{I J} (\partial_i \varphi^I) (\partial_j \varphi^J)$withtwoscalars$\varphi^I (I = 1, 2)$ used in Two Measure Theory (TMT). As in the flat-background case, the string tension $T=(2\pi {\alpha }^{\mathrm{\prime }}{)}^{-1}$ emerges as an integration constant for the A_i-field equation. This mechanism is further generalized to supermembrane theory, and to super p-brane theory, both on general curved backgrounds. This shows the universal applications of dynamical measure of TMT to general supersymmetric extended objects on general curved backgrounds.