Geometry of Membrane Sigma Models

摘要: String theory still remains one of the promising candidates for a unification gravity and quantum field theory. One its essential parts is relativistic description moving multi-dimensional objects called membranes (or p-branes) in curved spacetime. On classical level, they are described by an action functional extremalising volume manifold swept propagating membrane. This related theories collectively membrane sigma models. Differential geometry important mathematical tool study string It turns out that backgrounds can be conveniently using defined on direct sum tangent cotangent bundles spacetime manifold. Mathe- matical studying such object generalized geometry. Its integral part Leibniz algebroids, vector with algebra bracket module smooth sections. Special cases algebroids better known Lie Courant algebroids. This thesis divided into two main parts. In first one, we review foundations geometry, extended Nambu- Poisson structures. The aim to provide reader consistent introduction mathematics used published papers. text combination both well results new ones. We emphasize notion metric corresponding orthogonal transformations, which laid groundwork our research. second consists four attached papers treat selected topics articles presented same form as were published.