- Kharkov Institute of Physics and Technology, 310108, Kharkov, Ukraine
- 2 Supported in part by the International Science Foundation under the grant N RY 9000, by the State Committee for Science and Technology of Ukraine under the Grant N 2/100 and by the INTAS grants 93-127, 93-493, 93-633.
- Universitá Degli Studi Di Padova Dipartimento Di Fisica “Galileo Galilei”, ed INFN, Sezione Di Padova, Via F. Marzolo, 8, 35131 Padova, Italia
- 3 Supported in part by M.P.I. Work carried out as part of the European Community Programme “Gauge Theories, Applied Supersymmetry and Quantum Gravity” under contract SC1-CT92-D789.
- 4 On leave from Kharkov Institute of Physics and Technology, Kharkov, 310108, Ukraine.
- Kharkov Institute of Physics and Technology, 310108 Kharkov, Ukraine
We perform a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor-like formulation of super p-branes. Some basic features of the embedding world supersurface into target superspace specified by a geometrodynamical condition are considered. It is shown that the main attributes of the geometrical approach, such as the second fundamental form and extrinsic torsion of the embedded surface, and the Codazzi, Gauss and Ricci equations, have their doubly supersymmetric counterparts. At the same time the embedding of the supersurface into target superspace has its particular features. For instance, the embedding may cause more rigid restrictions on the geometrical properties of the supersurface. This is demonstrated with the examples of an N = 1 twistor-like supermembrane in D = 11 and type II superstrings in D = 10, where the geometrodynamical condition causes the embedded supersurface to be minimal and puts the theories on the mass shell.
- 1 - natural sciences ; 2 - physics & astronomy ; 3 - nuclear & particles physics
- 1 - sciences appliquees, technologies et medecines ; 2 - sciences exactes et technologie ; 3 - physique ; 4 - etat condense: structure, proprietes mecaniques et thermiques
- 1 - Physical Sciences ; 2 - Physics and Astronomy ; 3 - Nuclear and High Energy Physics