1963/03/01 by William M. Boothby, Shôshichi Kobayashi, H. C. Wang · 3 citations
Mathematics · #Holomorphic and Operator Theory #Geometry and complex manifolds #Geometric and Algebraic Topology
paper · doi:10.2307/1970219
openalex publication_date 1963/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
Let M and N be almost complex manifolds of class C and dimensions 2m and 2n respectively. We shall call a map f: M a N almost analytic if it is of class1 C3 and preserves the almost complex structure. Let ?(M, N), or simply A, denote the space of all such maps topologized by uniform convergence on compact sets of the mapping functions and their derivatives through the third order. When M = N, we denote by A(M) the set of elements of E which are diffeomorphisms (i.e., differentiable homeomorphisms with nowhere vanishing jacobian). These are easily seen to form a transformation group of M when topologized as subspace of A. With these definitions, we state the following three results: