Generalized Riemannian spaces

CONTENTS Introduction Chapter I. Basic concepts connected with the intrinsic metric § 1. Basic definitions § 2. General propositions on upper angles Chapter II. Spaces of curvature () § 3. Basic properties of an -domain § 4. Constructions § 5. Equivalent definitions of an -domain § 6. Area and the isoperimetric inequality § 7. Plateau's problem § 8. Spaces of curvature Chapter III. The space of directions § 9. The space of directions at a point in § 10. The tangent space Chapter IV. Spaces of bounded curvature § 11. Spaces of curvature both and § 12. Introduction of the Riemannian structure Chapter V. Smoothness of the metric in spaces of bounded curvature § 13. Parallel translation § 14. Smoothness of the metric References