TY - BOOK ID - 1394320 TI - Invariant forms on Grassmann manifolds PY - 1977 VL - 89 SN - 0691081980 0691081999 1400881889 9780691081991 9780691081984 PB - Princeton : Tokyo : Princeton University Press University of Tokyo press, DB - UniCat KW - Algebraic geometry KW - Differential geometry. Global analysis KW - Grassmann manifolds KW - Differential forms. KW - Grassmann manifolds. KW - Invariants. KW - Geometry, Differential. KW - Géométrie différentielle. KW - Differential invariants. KW - Invariants différentiels. KW - Forms, Differential KW - Continuous groups KW - Geometry, Differential KW - Grassmannians KW - Differential topology KW - Manifolds (Mathematics) KW - Calculation. KW - Cohomology ring. KW - Cohomology. KW - Complex space. KW - Cotangent bundle. KW - Diagram (category theory). KW - Exterior algebra. KW - Grassmannian. KW - Holomorphic vector bundle. KW - Manifold. KW - Regular map (graph theory). KW - Remainder. KW - Representation theorem. KW - Schubert variety. KW - Sesquilinear form. KW - Theorem. KW - Vector bundle. KW - Vector space. KW - Géométrie différentielle. KW - Invariants différentiels. UR - https://www.unicat.be/uniCat?func=search&query=sysid:1394320 AB - This work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann manifold is of importance for the construction of Chern classes of complex vector bundles. The cohomology ring of a Grassmannian is therefore of interest in topology, differential geometry, algebraic geometry, and complex analysis. Wilhelm Stoll treats certain aspects of the complex analysis point of view.This work originated with questions in value distribution theory. Here analytic sets and differential forms rather than the corresponding homology and cohomology classes are considered. On the Grassmann manifold, the cohomology ring is isomorphic to the ring of differential forms invariant under the unitary group, and each cohomology class is determined by a family of analytic sets. ER -