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Foreword; Preface; Contents; 1 De Sitter Relativity: A Sixty-Year-Long Story; 1.1 Introduction; 1.2 Historical Origins; 1.3 Later Developments; 1.4 PSR as a "Dual" Theory; 1.5 Experimental Verification; 1.6 De Sitter Observers, Singularities and Wick Rotations; 1.7 De Sitter Relativity in Current Research; 1.8 De Sitter Space and Field Theory; References; 2 Steps Towards the De Sitter Relativity; 2.1 Some Recalls About Lie Groups; 2.2 Lie Groups of Spacetime; 2.3 The Fantappié "Erlangen Program"; 2.4 The Arcidiacono Transformations; 2.5 Some Consequences; References.
3 Projective Special Relativity3.1 Preliminary Considerations; 3.2 The Principle of Relativity; 3.3 Hyperspheric Prespace; Reference; 4 Point, Fluid and Wave Mechanics; 4.1 Introduction; 4.2 PSR Metric; 4.3 Kinematics of the Material Point; 4.4 Dynamics of the Material Point; 4.5 Dynamics of Perfect Incompressible Fluids; 4.6 Digression on the Concept of Temperature in PSR; 4.7 Dynamics of Perfect Incompressible Fluids with Heat Exchange; 4.8 D'Alembert Equation; 4.9 The Meaning of Physical Quantities in PSR; 4.10 Concluding Notes; References; 5 Cosmic Electromagnetism.
5.1 Electromagnetic Equations in PSR5.2 Relativistic Transformation of Electromagnetic Quantities (in the Framework of PSR); References; 6 Projective General Relativity (PGR); 6.1 From PSR to PGR; 6.2 Arcidiacono's Construction; 6.3 Local Applications of PGR; 6.4 Consistency Issues; 6.5 The Cosmological Problem; 6.6 Initial Singularity and Horizon; 6.7 Archaic Universe; 6.8 The Origin of Inertia; 6.9 Dark Matter; 6.10 The Dominance of Matter; References; Appendix A; Curvature and Torsion in PGR; Appendix B: Interlude; Some Remarks About the Current Status of Cosmological Problem; Index.
3 Projective Special Relativity3.1 Preliminary Considerations; 3.2 The Principle of Relativity; 3.3 Hyperspheric Prespace; Reference; 4 Point, Fluid and Wave Mechanics; 4.1 Introduction; 4.2 PSR Metric; 4.3 Kinematics of the Material Point; 4.4 Dynamics of the Material Point; 4.5 Dynamics of Perfect Incompressible Fluids; 4.6 Digression on the Concept of Temperature in PSR; 4.7 Dynamics of Perfect Incompressible Fluids with Heat Exchange; 4.8 D'Alembert Equation; 4.9 The Meaning of Physical Quantities in PSR; 4.10 Concluding Notes; References; 5 Cosmic Electromagnetism.
5.1 Electromagnetic Equations in PSR5.2 Relativistic Transformation of Electromagnetic Quantities (in the Framework of PSR); References; 6 Projective General Relativity (PGR); 6.1 From PSR to PGR; 6.2 Arcidiacono's Construction; 6.3 Local Applications of PGR; 6.4 Consistency Issues; 6.5 The Cosmological Problem; 6.6 Initial Singularity and Horizon; 6.7 Archaic Universe; 6.8 The Origin of Inertia; 6.9 Dark Matter; 6.10 The Dominance of Matter; References; Appendix A; Curvature and Torsion in PGR; Appendix B: Interlude; Some Remarks About the Current Status of Cosmological Problem; Index.