CONTENTS -- Preface -- The Deligne-Simpson Problem for Zero Index of Rigidity -- 1 Introduction -- 2 Definitions and known facts -- 3 The basic result -- 4 Proof of Theorem 14 -- 5 Case A) -- 6 Case C) -- 7 Case B) -- 8 Case D) -- 9 Proof of Theorem 15 in the case of matrices Aj -- References -- Theorems for Extension on Manifolds with Almost Complex Structures -- 1 Introduction -- 2 Hahn-Banach type theorems -- 3 Proofs -- 4 Extension of invariant differential forms -- References -- The Theorem on Analytic Representation on Hypersurface with Singularities -- References -- Pseudogroup Structures on Spencer Manifolds -- 1 Recall of definitions -- 2 Pseudogroup structures -- 3 T-manifolds integrability of (M J) -- 4 T-coherency -- 5 Perspectives -- References -- Type-Changing Transformations of Hurwitz Pairs Quasiregular Functions and Hyper Kahlerian Holomorphic Chains I -- 1 Introduction -- 2 Dualities -- 3 Complementarity -- References -- Embedding of the Moduli Space of Riemann Surfaces with Igeta Structures into the Sato Grassmann Manifold -- 1 Introduction -- 2 Preliminaries -- 3 Embedding and IGL1(C)-actions -- References -- On the Quotient Spaces of S2 x S2 under the Natural Action of Subgroups of D4 -- 1 Introduction -- 2 Notation -- 3 The quotient spaces in Massey's diagram -- 4 Other quotient spaces in the complete diagram -- 5 Problems -- Acknowledgments -- References -- Existence of Spin Structures on Cyclic Branched Covering Spaces over Four-Manifolds -- 1 Introduction -- 2 Preliminaries -- 3 Proof of Theorem 1.1 -- References -- Length Spectrum of Geodesic Spheres in Rank One Symmetric Spaces -- 1 Introduction -- 2 Geodesic spheres and tubes around hyperplanes -- 3 Length spectrum from qualitative viewpoint -- 4 Length spectrum from quantitative viewpoint -- 5 Structure torsion of geodesics.

6 Congruency of geodesics -- 7 Sketch of Proofs -- Acknowledgment -- References -- Grassmann Geometry of 6-Dimensional Sphere II -- Introduction -- 1 Preliminaries -- 2 J-holomorphic curves -- 3 3-dimensional submanifolds -- 4 4-dimensional submanifolds -- References -- Hypersurfaces in Euclidean Space which are One-Parameter Families of Spheres -- 1 Introduction -- 2 Spheres of codimension two in Euclidean space -- 3 One-parameter families of spheres of codimension two in En + 1 -- References -- Hypersurfaces of Conullity Two in Euclidean Space which are One-Parameter Systems of Torses -- 1 Preliminaries -- 2 Hypersurfaces of conullity two in Euclidean space -- 3 Torses in Euclidean space -- 4 Hypersurfaces of conullity two and one-parameter systems of torses -- References -- Real Hypersurfaces of a Kaehler Manifold (the Sixteen Classes) -- 1 Introduction -- 2 The sixteen possible classes of real hypersurfaces of a Kaehler manifold -- 3 Examples -- References -- Almost Contact B-Metric Hypersurfaces of Kaehlerian Manifolds with B-Metric -- Introduction -- 1 Preliminaries -- 2 Time-like hypersurfaces of an almost complex manifold with B-metric -- 3 Isotropic hypersurfaces regarding the associated metric of an almost complex manifold with B-metric -- References -- Projective Formalism and Some Methods from Algebraic Geometry in the Theory of Gravitation -- 1 Introduction and statement of the investigated problem -- 2 First and Second Differentials and Variations -- 3 Formulation of the Variational Problem in the Case of Different Operators of Variation and Differentiation -- 4 First Variation of the Lagrangian as a Third-Rank Polynomial -- 5 Third-Rank Polynomials - Formulation of the Problem from an Algebro-Geometric Point of View -- References -- Geometry of Manifolds and Dark Matter -- 1 Introduction.

2 Geometrical framework -- 3 Symmetry -- 4 Main Conjecture -- 5 Field Equations -- 6 General Physical Interpretation -- 7 Summary -- References -- Lagrangian Fluid Mechanics -- 1 Introduction -- 2 Lagrangian density and Lagrangian invariant -- 3 Euler-Lagrange's equations for the variables on which the pressure p depends -- 4 Energy-momentum tensors for a fluid with pressure p -- 5 Special cases -- 6 Conclusion -- References -- Transformation of Connectednesses -- 1 Preliminary -- 2 (v)-Corresponding Affine Connectedness -- 3 Mutual Connectedness -- References.