Thesis (doctoral)--Universität Bonn, 1993. / Includes bibliographical references (p. 58-61).

Inaug. Diss.--Bonn. / Includes bibliographical references.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1995. / Includes bibliographical references (p. [57]).

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 62-64).

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves [145-147]).

When computing the homology of Grassmannian manifolds, the first step is usually to look at the Schubert cell decomposition, and the chain complex associated with it. In the complex case and the real unoriented case with Z₂ coefficients the additive structure is obtained immediately (i.e., generated by the homology classes represented by the Schubert cells) because the boundary map is trivial. In the real unoriented case (with Z₂ coefficients) and the real oriented case, finding the additive structure is more complicated since the boundary map is nontrivial. In this paper, this boundary map is computed by cell orientation comparisons, using graph coordinates where the cells are linear, to simplify the comparisons. The integral homology groups for some low dimensional oriented and unoriented Grassmannians are determined directly from the chain complex (with the boundary map as computed). The integral cohomology ring structure for complex Grassmannians has been completely determined mainly using Schubert cell intersections (what is known as Schubert Calculus).. In this paper, a method using Schubert cell intersections to describe the Z₂ cohomology ring structure of the real Grassmannians is sketched. The results are identical to those for the complex Grassmannians (with coefficients), but the notation used for the cohomology generators is not the usual one. It indicates that the products are to a certain degree independent of the Grassmannian. / Science, Faculty of / Mathematics, Department of / Graduate

by Tsang Yau Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 79-83). / Contents --- p.1 / Chapter Chapter 0 --- Introduction --- p.1 / Chapter Chapter 1. --- Elliptic Case --- p.4 / Chapter 1.1 --- Existence of energy minimizing maps --- p.6 / Chapter 1.2 --- Complex analyticity of energy minimizing maps --- p.9 / Chapter 1.3 --- Holomorphic deformation of rational curves --- p.15 / Chapter 1.4 --- End of proof and further remarks --- p.25 / Chapter Chapter 2. --- Parabolic Case --- p.30 / Chapter 2.1 --- Construction of non-vanishing holomorphic n-form --- p.32 / Chapter 2.2 --- Construction of functions of minimal degree --- p.50 / Chapter 2.3 --- Construction of biholomorphism using minimal degree functions --- p.53 / Chapter Chapter 3. --- Hyperbolic Case --- p.59 / Chapter 3.1 --- Various types of negative curvature conditions --- p.61 / Chapter 3.2 --- A Bochner type identity --- p.63 / Chapter 3.3 --- Complex analyticity of harmonic maps --- p.66 / Chapter 3.4 --- Bounded symmetric domains --- p.73 / Chapter 3.5 --- "Strong ""rigidity"" and other applications" --- p.76 / Bibliography --- p.79

Low, Ho Chi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 76-79). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Zhang Yi. / "May 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 141-146). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 2003. / Includes bibliographical references. Also available on the Internet.