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

by Sekigawa, Kouei; Gerdjikov, Vladimir S.; Matsushita, Yasuo; Mladenov, Ivaïlo M.

• ISBN13: 9780735408951
• ISBN10: 0735408955
• Format: Paperback
• Copyright: 2011-07-20
• Publisher: Amer Inst of Physics

Summary

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 Kähler 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.

Table of Contents

Preface	p. 1
Photograph	p. 4
The language of mathematics	p. 5
Geometry And Complex Structures
Initial value problem for the double-complex Laplace operator. Eigenvalue approaches	p. 15
On the homology defined by the electromagnetic energy tensor	p. 23
Geometry of pre-contrast functions and non-conservative estimating functions	p. 32
A mathematical base for fiber bundle formulation of Lagrangian quantum field theory	p. 42
A note on a homogeneous structure on an almost contact metric space	p. 53
Linear Weingarten surfaces in hyperbolic three-space	p. 58
Geometric structures in four-dimension and almost Hermitian structures	p. 66
On some deformations of the Cassinian oval	p. 81
Closed hypersurfaces in Riemannian manifolds whose second fundamental forms are of constant length	p. 90
Complex connections on conformal Kähler manifolds with Norden metric	p. 97
Integrability and Vector Fields
Multicomponent nonlinear systems of Bose-Fermi fields: Exact solutions	p. 111
Travelling waves for some generalized Boussinesq types equations	p. 126
An optimal system of one-dimensional symmetry Lie algebras of coupled nonlinear Schrödinger equations	p. 134
Collision dynamics of polarized solitons in linearly coupled nonlinear Schrodinger equations	p. 144
On certain reductions of integrable equations on symmetric spaces	p. 154
Quadratic Casimir invariants for "Universal" Lie algebra extensions	p. 165
Mechanics And Mathematical Physics
Two basic uncertainty relations in quantum mechanics	p. 183
Analytic description of the equilibrium shapes of elastic rings under uniform hydrostatic pressure	p. 189
Minimizers of Hartree type functionals and related interpolation inequalities	p. 203
An approach for computing the Euclidean motions on the base of measurement data	p. 212
Dynamical invariants and Robertson-Schrödinger correlated states of electromagnetic field in nonstationary linear media	p. 221
Cell membranes under hydrostatic pressure subjected to micro-injection	p. 234
List of Participants and Contributors	p. 241
Author Index	p. 245
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