The theory of topological sheaves (see 2.2) and the implicit function theorem (see 2.3) provide a general framework for the isometric immersion problem which consists of the construction and classification of isometric C ∞-maps f: (V, g) → (W, h), for given forms g on V and h on W (compare 2.4.9). However, the direct application of 2.2 and 2.3 does not lead to geometrically significant results unless specific geometrical features of the forms in question are taken into account.
KeywordsRiemannian Manifold Sectional Curvature Constant Curvature Symplectic Form Implicit Function Theorem
Unable to display preview. Download preview PDF.