International Workshop on Complex Structures, Integrability and Vector Fields : Sofia, Bulgaria, 13-17 September 2010

The present workshop is aiming at the higher achievement of the studies of current topics ranging over differential geometry, complex analysis and mathematical physics their future developments and their numerous applications. The present volume provides useful and significant information to the specialists in differential geometry, complex analysis and mathematical physics. It will be interesting also to a much broader audience of scholars and scientists working or interested in classical and quantum mechanics, in cell membranes, integrability and soliton interactions etc. Its geometric part includes homogeneous structures on almost contact metric spaces, geometric structures in four-manifolds and almost hermitian structures, complex connections on conformal Kahler manifolds, existence of compact hypersurfaces with the second fundamental form of constant length, linear Weingarten surfaces in a hyperbolic three-space, pre-contrast functions and their geometric properties, and further, fibre bundle formulation of Lagrangian quantum field theory, curvature forms and interaction of fields concerning geometrical setting in mathematical physics. The part on integrability and vector fields is devoted to the study of multicomponent nonlinear Schrodinger (MNLS) equations which play important role for understanding hydro-dynamical processes, the phenomena of Bose-Einstein condensates, etc. The symmetries of these MNLS equations are also studied, as well as their reductions and Lie algebraic properties. The third part of these proceedings treats problems of contemporary mechanics and mathematical physics. The methods of differential geometry quite unexpectedly provide important tool for modeling and studying microinjections in cell membranes, the equilibrium.