CONTENTS -- Preface -- Contributed Communications -- Geodesics and trajectories for Kahler magnetic fields T. Adachi -- 1. Introduction -- 2. Variations of trajectories -- 3. Variations of magnetic fields -- 4. Ruled real surfaces associated with trajectories -- 5. A comparison on crescents -- References -- Ordinary helices and Riemanninian geometry T. Adachi and S. Maeda -- 1. Introduction -- 2. Killing ordinary helices on nonflat complex space forms -- 3. Bounded Killing ordinary helices on a complex hyperbolic plane -- 4. Killing ordinary helices on other symmetric spaces of rank one -- 5. Characterization of real space forms by Killing ordinary helices -- 6. A construction of a closed non-Killing ordinary helix on CP"(c) -- References -- Real analyticity of the almost Kahler manifolds L. Apostolova -- 1. Introduction and some definitions -- 2. Canonical construction -- 3. Real analyticity of the almost Kahler manifolds -- References -- Isotropic immersions of rank one symmetric spaces into real space forms and mean curvatures N. Boumuki -- 1. Introduction -- 2. Terminology -- 3. Isotropic immersions of a sphere into a real space form -- 4. Isotropic immersions of a complex space form into a real space form -- 5. Isotropic immersions of Cayley projective plane into a real space form -- References -- Bi-complex holomorphicity S. Dimiev and S. Slavova -- 1. Introduction -- 2. Even dimensional real anti-cyclic numbers -- 3. Abstract derivative of Scheffers -- 4. Holomorphic functions on C [1,j] -- 5. *-type interpretation -- 6. Cauchy's integral formula -- 7. Bi-complex analytic functions -- 8. Singularities -- 9. Generalizations -- References -- Generalized parallelism and field equations S. Donev and M. Tashkova -- 1. Definition of the General Parallelism Concept -- 2. The GPR in Action -- 2.1. Classical mechanics.

2.1.1. Integral invariance relations -- 2.1.2. Absolute and relative integral invariants -- 2.1.3. Symplectic mechanics -- 2.2. Frobenius integrability theorems and linear connections -- 2.2.1. Frobenius integrability theorems -- 2.2.2. Linear connections -- 2.2.3. Covariant exterior derivative -- 3. Physical applications of GPR -- 3.1. Autoparallel vector fields and 1-forms -- 3.2. Electrodynamics -- 3.2.1. Maxwell equations -- 3.2.2. Extended Maxwell equations -- 3.3. Yang-Mills equations -- 3.3.1. Extended Yang-Mills equations -- 3.4. General Relativity -- 3.5. Schrodinger equation -- 3.6. Dirac equation -- 4. Conclusion -- References -- Stable simply connected minimal surfaces in RN and SO(N, C)-action N. Ejiri -- 1. Introduction -- 2. Complex subspaces in RN -- 3. The definition of s-isotropic minimal surfaces -- 4. A deformation by SO(N, C) -- 5. A proof of Theorem -- References -- Multiple scale procedure in Laplace transform space for solution of weakly nonlinear wave equation A. Golbabai -- 1. Introduction -- 2. The Procedure -- 3. Examples of non-linear boundary value problems for wave equations -- 3.1. Non linearities of the form f(ux) -- 3.2. Non linearity of the form f(ut) -- 3.3. Nonlinearity of the form f(u), f(u) -- References -- Orthogonal compositions in a four-dimensional Weyl space D.K. Gribacheva -- 1. Preliminaries -- 2. Orthogonal compositions in a four-dimensional Weyl space -- 3. Properties of the curvature tensor on a four-dimensional Weyl product space -- References -- On a fibre bundle formulation of classical statistical mechanics B. Iliev -- 1. Introduction -- 2. Hamilton description of classical mechanics (review) -- 3. Bundle description of dynamical functions in classical mechanics -- 4. Bundle description of the Liouville equation -- 5. Conclusion -- References.

Existence of indefinite Kahler metrics of constant scalar curvature on compact complex surfaces H. Kamada -- 1. Introduction -- 2. Preliminaries -- 3. Obstructions -- 4. Kahler surfaces -- 4.1. Ricci-flat case -- 4.2. Einstein case -- 4.3. Scalar-flat case -- 4.4. Constant scalar curvature case -- 5. Problems and questions -- Acknowledgment. -- References -- Projecive Bkzier curves of order 2 on real space forms S. Kawabata and T. Adachi -- 1. Introduction -- 2. BQzier curves -- 3. Rational BQzier curves -- 4. Projective Bezier curves on a standard sphere -- 5. Projective Bezier curves on a real hyperbolic plane -- References -- Canonical metrics and Harder-Narasimhan filtration J. Keller -- 1. Background material for stability of vector bundles -- 2. Gieseker stability and canonical metrics -- 3. Harder-Narasimhan filtration -- 4. The case of surfaces -- References -- Totally umbilic hypersurfaces and isoparametric hypersurfaces in space forms M. Kimura and S. Maeda -- 1. Introduction In differential geometry it is interesting to -- 2. Characterization of totally umbilic hypersurfaces I -- 3. Characterizations of isoparametric hypersurfaces -- 4. Characterization of totally umbilic hypersurfaces II -- References -- Type-changing transformations of Hurwitz pairs, quasiregular functions, and hyper-Kahlerian holomorphic chains J. Lawrynowicz, M. Nowak and L. Tovar -- 1. Introduction -- 2. Branch-type fractal representation and Atomization Theorem for Hermitian Hurwitz pairs -- 3. Fractal gemmae, their type-changing transformations and the corresponding Atomization Theorem -- 4. Relationship with hyperkahlerian holomorphic chains -- References -- Some four-dimensional almost hypercomplex pseudo-Hermitian manifolds M. Manev and K. Sekigawa -- Introduction -- 1. The two known examples of almost (H, G)-manifolds.

1.1. A pseudo-Riemannian spherical manifold with ( H, G ) -structure -- 1.2. The Thurston manifold with ( H, G)-structure -- 2. Engel manifolds with almost ( H, G)-structure -- 2.1. Double isotropic hyper-Kahlerian structures but neither hypercomplex nor symplectic -- 2.2. Double isotropic hyper-Kahlerian structures which are non-integrable but symplectic -- 3. Real spaces with almost ( H, G)-structure -- 3.1. Real semi-space with almost ( H, G)-structure -- 3.2. Real quarter-space with almost ( H, G ) -structure -- 4. Real pseudo-hyper-cylinder with almost ( H, G)-structure -- 5. Complex surfaces with almost ( H, G)-structure -- 5.1. Complex cylinder with almost ( H, G)-structure -- 5.2. Complex cone with almost ( H, G ) -structure -- 5.3. Complex sphere with almost ( H, G)-structure -- 6. Lie groups with almost ( H, G)-structure -- 6.1. A Lie group as a complex manifold but non-hypercomplex one -- 6.2. A Lie group as a flat Kahler manifold but non-hypercomplex one -- Acknowledgement -- References -- Navier-Stokes' equations for radial and tangential accelerations S. Manoff -- 1. Introduction -- 2. Navier-Stokes' identities and Navier-Stokes' equations -- 3. Invariant projections of Navier-Stokes' equations -- 3.1. Navier-Stokes' equations and Euler-Lagmnge's equations -- 3.2. Representation of F and -- 3.3. Radial projections of Navier-Stokes' equation. Navier-Stokes' equation for radial accelerations -- 3.4. Tangential projections of Navier-Stokes' equation. Navier-Stokes' equation for tangential accelerations -- 4. Conclusions -- References -- A quaternion approach in physics and engineering calculation V. Markova and V. Shopov -- 1. Introduction -- 2. Quaternionic solution of the inverse kinematics problem for planar robot -- 2.1. Quaternionic solution of the inverse kinematics problem for a two link planar robot.

3. The molecule structure and discrete curves -- 3.1. Frenet frames in H -- 3.2. Standart protein geometry -- 4. The molecule kinematics model -- 5. Spherical linear interpolation -- 5.1. Interpolation using quaternions -- 5.2. Spherical linear interpolation -- 5.3. The numerical problem in ocasion of smal values of -- 5.4. Algorithm for using slerp in numerical engeneering calculation -- References -- The existence of indefinite metrics of signature (++--) and two kinds of almost complex structures in dimension four Y. Matsushita -- Acknowledgement. -- References -- On the complex WKB analysis for a 2nd order linear O.D.E. with the most general characteristic polygon M. Nakano -- 1. Introduction -- 2. The asymptotic reductions of (1.1) -- 3. The WKB approximations -- 4. Formal computation of matching matrices -- 5. Matching matrices for (1.1) -- References -- Speed and acceleration of projective Bkzier curves of order on real space forms T. Nonogaki and T. Adachi -- 1. Introduction -- 2. Bezier spline curves in a Euclidean space -- 3. Rational BQzier spline curves on a Euclidean plane -- 4. Projective BQzier spline curves on a standard sphere -- 5. Projective BQzier spline curves on a hyperbolic plane -- References -- A potential and catastrophe of a soap film T. Okamoto and N. Ejiri -- 1. Introduction -- 2. Conclusion -- 0bservation -- 3. A frame with two equilibrium shapes -- 4. Analysis of the catastrophe phenomenon of a soap film -- References -- Kinematics and vectorfields on differentiable spaces K. Spallek -- Einleitung -- 1. Vorbereitungen -- 2. Parametrische Familien von "Bewegungungen" . Allgemeine Bewegungsablaufe -- 3. Bewegungsablaufe und lokal integrable Felder auf Raumen -- 4. Gleitgleitkinematik, kinematische Unterraume -- 5. Geodatische Kinematik in Zahlenraumen Rn -- Literatur.

A computer-assisted study of the delayed logistic map K. Takahashi.