CONTENTS -- Preface -- CONTRIBUTORS -- On g-natural metrics with constant scalar curvature on unit tangent sphere bundles M.T.K. Abbassi and O. Kowalski -- Introduction and main results -- 1. Basic formulas on tangent bundles -- 2. Riemannian metrics on T1M induced from Riemannian g-natural metrics on TM of the form a.gs + b.gh + c.gv -- 3. Proofs of the main results -- References -- Magnetic mean operators on a Kahler manifold T. Adachi -- 1. Introduction -- 2. Magnetic mean operators -- 3. Expansion of magnetic means with respect to radius -- 4. Magnetic trajectory chains -- References -- Yang-Mills fields analogue of biharmonic maps C. Bejan and H. Urakawa -- 1. Introduction -- 2. Biharmonic submanifolds and maps -- 3. Bi-Yang-Mills fields -- References -- Invariant and anti-invariant unit vector fields T.Q. Binh, E. Boeckx and L. Vanhecke -- 1. Introduction -- 2. Preliminaries -- 3. Submanifolds generated by unit vector fields -- References -- A new structure on unit tangent sphere bundles J.T. Cho and S.H. Chun -- 1. Introduction -- 2. Oproiu's structure on tangent bundles -- 3. A new structure on unit tangent sphere bundles -- References -- Application of Bochner- Weizenbock formulas to symplectic and complex pairs to be Kahler pairs in dimension four I. Garcia-Ramirez, E. Garcia&Rio and Y. Matsushita -- 1. Introduction -- 2. Symplectic pairs, complex pairs and Kahler pairs -- 2.1. Symplectic pairs -- 2.2. Complex pairs -- 2.3. Kahler pairs -- 3. Curvature conditions for a DAH 4-manifold to be DK -- 3.1. Symplectic pairs and sectional curvatures -- 3.2. Complex pairs of nonpositive sectional curvature -- 3.3. Mized pairs -- References -- Complete K-curvature homogeneous pseudo-Riemannian manifolds 0-modeled on an indecomposible symmetric space P. Gilkey and S. Nikcevic -- 1. Introduction -- 1.1. Affine manifolds.

1.2. Pseudo-Riemannian manifolds -- 1.3. Various notions of homogeneity -- 1.4. Previous results -- 1.5. Curvature homogeneity and homogeneity -- 1.6. Scalar invariants -- 1.7. Riemannian manifolds modeled on homogeneous spaces -- 1.8. The pseudo-Riemannian manifolds M6+4p,f -- 1.9. The geometry of the manifolds M6+4p,f -- 1.10. The symmetric space S6+4p -- 1.11. The homogeneous spaces 6+4p,k -- 1.12. The manifolds N6+4p, -- 1.13. Curvature and affine homogeneity -- 2. Completeness -- 3. A 0-model for M6+4p,f -- 3.1. Models for the manifolds M6+4p,f -- 4. Isometries -- Acknowledgments -- References -- Miyaoka-Yau inequality and complex hyperbolicity M. Itoh -- 1. Main Theorems -- 2. The modified scalar curvature and the L2-curvature inequality -- 3. The self-dual Weyl curvature and the Kahler-Einstein condition -- 4. Proof of Theorem 1 -- 5. Proof of Theorem 2 -- References -- Neutral bi-Hermitian Gray surfaces W. Jelonek -- 0. Introduction -- 1. Neutral AC -surfaces -- 2. Neutral bi-Hermitian Gray surfaces -- 3. Einstein neutral bi-Hermitian surfaces -- 4. Neutral Kahler Gray surfaces -- References -- On the discontinuity of affine motions and Auslander's conjecture T. Kawabe -- Introduction -- 1. Affine crystallographic subgroup of Aff(2) -- 2. A Contractive affine action on a R6 -- 3. Levi factor SO(3,2) -- 4. A remark on the Auslander's conjecture -- References -- Real hypersurfaces in non-flat complex space forms concerned with the structure Jacobi operator and Ricci tensor U-H. Ki, S. Nagai and R. Takagi -- 0. Introduction -- 1. Fundamental facts of real hypersurfaces -- 2. The Jacobi operator of real hypersurfaces -- 3. Lemmas -- 4. Theorems -- References -- Real hypersurfaces in a nonflat complex space form from the viewpoint of their geodesics S. Maeda and T. Adachi -- 1. Introduction -- 2. Real hypersurfaces in a nonflat complex space form.

3. Extrinsic shape of geodesics on standard examples -- 4. Characterizations of standard real hypersurfaces -- References -- Tangent bundles with Sasaki metric and almost hypercomplex pseudo-Hermitian structure M. Manev -- Introduction -- 1. Some Kinds of Differentiable Manifolds with Almost Complex Structures -- 1.1. Almost Complex Manifolds with Hermitian Metric or Skew-Hermitian Metric -- 1.2. Almost Hypercomplex Manifolds with Pseudo-Hermitian Structure -- 2. The Tangent Bundle -- 2.1. Vertical Lifts -- 2.2. Horizontal Lifts -- 2.3. Adapted Frames -- 3. The Tangent Bundle with an Almost Hypercomplex Pseudo-Hermitian Structure -- 3.1. An Almost Hypercomplex Structure on the Tangent Bundle -- 3.2. The Sasaki Metric on the Tangent Bundle -- 3.3. The Tangent Bundles with Almost Hemitian, Almost Skew-Hemitian and Almost Hypercomplex Pseudo-Hemitian Structures -- 4. Eight-Dimensional Derived Examples -- Acknowledgement -- References -- On the existence of 3-dimensional invariant submanifolds of S6 K. Mashimo -- 1. Preliminaries -- 2. Existence of Ex-submanifold -- References -- Infinitesimal Fourier transformation for the space of functionals T. Nitta and T. Okada -- 0. Introduction -- 1. Formulation -- 2 Proofs of Theorems -- 3. Examples -- Acknowledgement. -- References -- A Liouville theorem for harmonic maps with finite total n-energy T. Okayasu -- 1. Introduction -- 2. Proof -- References -- On a family of almost Kahler structures on the tangent bundles over some statistical models T. Sato -- 1. Introduction -- 2. Statistical models -- 2.1. Normal distributions -- 2.2. Discrete distributions on finite X -- 3. Almost Kahler structures on the tangent bundle -- 4. -family of almost Kahler structures on TS -- 4.1. Tangent budle of the manifold of normal distributions -- 4.2. Tangent budle of the statistical model of discrete distributions.

References -- Recent progress on real hypersurfaces in complex two-plane Grassmannians Y.J. Suh -- 1. Riemannian geometry of G2(Cm+2) -- 2. Some fundamental formulas for real hypersurfaces in G2(Cm+2) -- 3. Recent results for real hypersurfaces in G2(Cm+2) -- References -- Curvature of the determinant line bundle on the moduli space of null-correlation bundles T. Taniguchi -- 1. Introduction -- 2. Preliminaries -- 3. The moduli space of null-correlation bundles over CP3 -- 4. Diffeo-type and tangent space of null-correlation bundles -- 5. Metric on M(HP2) -- 6. Main Theorem -- References -- Isotropic Kahler immersions into a complex quadric K. Tsukada -- 1. Introduction -- 2. The complex conformal structure on a complex quadric and isotropic Kahler immersions -- 3. Isotropic Kahler immersions of Hermitian symmetric spaces -- References -- Professor Kouei Sekigawa and his friends in mathematics Y. Matsushita -- References.