CONTENTS -- Preface -- Organizing Committee -- Contributed Communications -- Moduli space of Killing helices of low orders on a complex space form T. Adachi -- 1. Introduction -- 2. Moduli space of Killing helices and length spectrum -- 3. Moduli space of helices on a real space form -- 4. Moduli space of circles on a complex space form -- 5. Moduli spaces of Killing helices of orders less than 5 on a complex space form -- 6. Lamination on moduli space of essential Killing helices -- Acknowledgments -- References -- Type two Killing helices of proper order four on a complex projective plane T. Adachi and S. Maeda -- 1. Introduction -- 2. Killing helices of proper order 4 -- 3. Type 2 Killing helices -- 4. Limit curves -- References -- Real analyticity of the hyperkahler almost Kähler manifolds L.N. Apostolova -- 1. Preliminaries -- 2. Real analyticity of a smooth manifold with two symplectic-homotopic symplectic forms ω0 and ω1 -- 3. Polarization of a symplectic form -- 4. Real analyticity of the hyperkahler almost Kähler manifolds -- References -- KCC and linear stability for the Parkinson tremor model V. Balan -- 1. The neural 3-unit feedback model -- 2. The covariant extension. Structural stability -- 3. Linear and KCC stability -- 4. The second-order Lagrangian extension -- Acknowledgement -- References -- The Camassa-Holm equation as a geodesic .ow for the H1 right-invariant metric A. Constantin and R.I. Ivanov -- 1. Motion of a rigid body with a .xed point - the SO(3) example -- 2. Camassa-Holm equation - right invariant metric on the diffeomorphism group -- 3. Inverse Scattering for the CH equation -- 4. Soliton solutions and the diffeomorphisms -- Acknowledgments -- References -- Fermi-Walker parallel transport, time evolution of a space curve and the Schrödinger equation as a moving curve R. Dandoloff.

I. Space curves, parallel transport and anholonomy. -- II. Lamb formalism, geometric phase and gauge potential. -- References -- Remarks on bicomplex variables and other similar variables S. Dimiev, R. Lazov and S. Slavova -- 1. Historical notes -- 2. Bicomplex and similar variables - a short recall -- 3. Real matrix representation of C(1, j) and C(1, j, j2, j3) -- 4. Complex quadratic geometries over C(1, j) and C(1, j, j2, j3) -- References -- Integrability, curvature and description of photon-like objects S. Donev and M. Tashkova -- 1. Introduction -- 2. Modelling Photon-like Objects -- 3. Physical Interpretation -- 4. Conclusion -- References -- Complex submanifolds and Lagrangian submanifolds associate with minimal surfaces in tori N. Ejiri -- 1. Introduction -- 2. A review on a function with parameter -- 3. A function with parameter on the Siegel upper half space Hγ -- 4. Minimal surfaces in tori -- References -- About resonances for Schrödinger operators with short range singular perturbation V. Georgiev and N. Visciglia -- 1. Introduction -- 2. On the continuity of the operator R(λ ± i0) -- 3. Some preliminary computations -- 4. Proof of theorem 1.1 -- Acknowledgments -- References -- Soliton equations with deep reductions. Generalized Fourier transforms V. Gerdjikov, N. Kostov and T. Valchev -- 1. Introduction -- 2. Preliminaries -- 3. Wronskian relations and squared solutions -- 4. Completeness of the squared solutions -- 5. Expansions over the squared solutions -- 6. Hamiltonian formalism -- 7. Conclusions -- Acknowledgement -- References -- On some deformations of almost complex structures of 6-dimensional submanifolds in the octonions H. Hashimoto -- 1. Introduction -- 2. Clifford algebras, spinor groups and octonions -- 2.1. Clifford algebras and spinor groups -- 2.2. Spin (7)-structure equations -- 3. Gram-Schmidt process of Spin(7).

4. Invariants of Spin(7) -- 5. Homogeneous spaces related to Spin(7) -- 6. Deformations of some examples -- 6.1. On S2 × S4 -- 6.2. On 1-parameter family of embeddings from S2 × R4 to C -- 6.3. On 1-parameter family of embeddings from S1 × S2 × R3 to C -- References -- On the real hypersurfaces of locally conformally-Kähler manifolds M.J. Hristov -- 1. Preliminaries -- 1.1. Locally conformally Kähler manifolds -- 1.2. Contact conformally almost contact metric manifolds -- 2. Real hypersurfaces of locally conformally-Kähler manifolds -- References -- Normal frames and linear transports along paths in line bundles. Applications to classical electrodynamics B.Z. Iliev -- 1. Introduction -- 2. Linear transports along paths (brief review) -- 3. Normal frames for linear transports -- 4. Linear transports and normal frames in line bundles -- 5. Bundle description of the classical electromagnetic field -- 6. Normal and inertial frames -- 7. Conclusion -- References -- Existence and uniqueness results for the Schrödinger - Poisson system below the energy norm A.M. Ivanov and G.P. Venkov -- 1. Introduction -- 2. Local existence result in ˙H 1 2 -- 3. Global existence result in H 1 2 -- Acknowledgments -- References -- Double-complex quadratic forms B. Kiradjiev -- 1. Double-complex numbers and double-complex vectors -- 2. Bilinear and quadratic forms on Cn(1, j) -- 3. Double-complex holomorphic Q-orthogonal geometry -- 3.1. Double-complex holomorphicity -- 3.2. Q-orthogonal geometry -- 4. Complex-hermitian double-complex quadratic forms -- 5. Fourth-complex quadratic forms -- References -- Effects of finite arithmetic in numerical computations M.M. Konstantinov and P.H. Petkov -- 1. Introduction -- 2. Myths in computational practice -- 3. Bad and good computational practices -- 3.1. Floating-point computations -- 3.2. Computing determinants.

3.3. Solving linear algebraic equations -- 3.4. Rank determination -- 3.5. Solving algebraic equations -- 3.6. Computing eigenvalues of a matrix -- References -- Exact solutions of the manakov system N.A. Kostov -- 1. Introduction -- 2. Basic equations and solutions -- 3. Exact solutions of the Manakov system using Lax pairs method -- 4. Alternative Theta-functional integration -- 5. Conclusions -- Acknowledgements -- References -- The Manakov system as two moving interacting curves N.A. Kostov, R. Dandolo., V.S. Gerdjikov and G.G. Grahovski -- 1. Introduction -- 2. Preliminaries -- 2.1. The Manakov model -- 2.2. Soliton curves -- 3. Integration of the extended da Rios system -- 4. Extended da Rios-Betchov system -- 5. HF system is gauge equivalent to Manakov system -- 6. Conclusions -- Acknowledgements -- References -- Cluster sets and periodicity in some structure fractals J. Lawrynowicz, S. Marchiafava and M. Nowak-K¸epczyk -- 1. Introduction and statement of the periodicity theorem -- 2. Quaternions and octonions in the Cayley-Dickson construction -- 3. The case 2p 1, period 1. A fractal bundle of the ower type -- 4. The case: 2p 1, perpendicular lower convergence. Ovary and ovules -- 5. The case: 2p 1, perpendicular upper convergence. The pistil and stamens -- References -- Sectional curvatures of some homogeneous real hypersurfaces in a complex projective space S. Maeda and M. Kimura -- 1. Introduction -- 2. Preliminaries -- 3. Sectional curvatures of hypersurfaces of type A or type B -- 4. Pinching problems on sectional curvature of real hypersurfaces -- On three-parametric Lie groups as quasi-Kähler manifolds with killing Norden metric M. Manev, K. Gribachev and D. Mekerov -- Introduction -- 1. Almost complex manifolds with Norden metric -- 1.1. Preliminaries -- 1.2. Curvature properties -- 1.3. Isotropic Kähler manifolds.

2. Lie groups as quasi-Kähler manifolds with Killing Norden metric -- 3. The Lie group as a 6-dimensional W3-manifold -- 4. Geometric characteristics of the constructed manifold -- 4.1. The components of the tensor F -- 4.2. The square norm of ∇J -- 4.3. The components of R -- 4.4. The components of ρ and the value of τ -- 4.5. The sectional curvatures -- 4.6. The isotropic-Kählerian property -- References -- Application of unscented and extended Kalman filtering for estimating quaternion motion V. Markova -- 1. Introduction -- 2. Kalman's filters - short background -- 3. The Problem of Trajectory interpolation -- 4. Experimental Study -- 5. Conclusion -- References -- Counterexamples of compact type to the Goldberg conjecture and various version of the conjecture Y. Matsushita -- 1. The Goldberg conjecture -- 2. Noncompact type for almost Hermitian manifolds -- 3. Noncompact type for almost pseudo-Hermitian manifolds -- 4. Counterexamples of compact type for almost pseudo-Hermitian Walker 8-manifolds -- 5. Almost Norden manifolds -- 6. Almost para-Hermitian manifolds -- 7. Odd-dimensional manifolds -- References -- Dispersion and asymptotic profiles for Kirchhoff equations T. Matsuyama and M. Ruzhansky -- 1. Introduction -- 2. Results -- 3. Representation of solutions to linear Cauchy problems -- References -- Geometry of statistical manifolds and its generalization H. Matsuzoe -- Introduction -- 1. Dual connections -- 2. Statistical manifolds -- 3. A generalization of statistical manifolds -- Acknowledgement -- References -- On some non-integrable almost contact manifolds with norden metric of dimension 5 G. Nakova -- Introduction -- 1. Almost contact manifolds with Norden metric -- 1.1. Preliminaries -- 1.2. Curvature properties -- 2. Lie groups as almost contact manifolds with Norden metric.

3. A Lie group as a 5-dimensional almost contact manifold with Norden metric of the class F9.