Complex Manifolds
Mostrando 13-20 de 20 artigos, teses e dissertações.
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13. HOMOGENEOUS COMPLEX MANIFOLDS AND REPRESENTATIONS OF SEMISIMPLE LIE GROUPS*
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14. EXAMPLES OF SINGULAR NORMAL COMPLEX SPACES WHICH ARE TOPOLOGICAL MANIFOLDS*
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15. Complex-analyticity of harmonic maps and strong rigidity of compact Kähler manifolds
A harmonic map f between two compact Kähler manifolds is shown to be either holomorphic or conjugate holomorphic under a suitable negativity condition on the curvature of the image manifold and a condition on the rank of df. As a consequence, a compact Kähler manifold of dimension ≥2 that is of the same homotopy type as a compact Kähler manifold with su
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16. On the structure of complete simply-connected Kähler manifolds with nonpositive curvature
We prove that a complete simply-connected Kähler manifold with nonpositive sectional curvature is biholomorphic to the complex Euclidean space if the curvature is suitably small at infinity.
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17. Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature
To study C0a priori estimates for solutions to certain complex Monge—Ampère equations, I introduce a coherent sheaf of ideals and show that it satisfies various global algebrogeometric conditions, including a cohomology vanishing theorem. This technique is used to establish the existence of Kähler-Einstein metrics of positive scalar curvature on a very l
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18. Local analytic hypoellipticity for □b on nondegenerate Cauchy—Riemann manifolds
The local real analytic regularity of solutions to □b, the complex boundary Laplacian, and related operators is proved for (p,q) forms on a nondegenerate, abstract, real analytic Cauchy-Riemann (C-R) manifold of dimension 2n - 1 satisfying J. J. Kohn's condition Y(q). The problem is reduced to the study of general, “variable coefficient” operators, sat
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19. Pseudoconformal Geometry of Hypersurfaces in Cn+1
The pseudoconformal geometry (CR structure) of a real hypersurface M in Cn+1 is reviewed. We give an alternative formulation of a theorem of Cartan-Tanaka-Chern on the existence of a unique normalized Cartan connection on a principal bundle Y over M. A family of curves defined by this connection, called chains, is shown to be the projection of light rays of
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20. A self-organizing principle for learning nonlinear manifolds
Modern science confronts us with massive amounts of data: expression profiles of thousands of human genes, multimedia documents, subjective judgments on consumer products or political candidates, trade indices, global climate patterns, etc. These data are often highly structured, but that structure is hidden in a complex set of relationships or high-dimensio
National Academy of Sciences.