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Series in Pure Mathematics - Vol. 6
METRIC RIGIDITY THEOREMS ON HERMITIAN LOCALLY SYMMETRIC MANIFOLDS
by Ngaiming Mok (Columbia Univ.)
This monograph studies the problem of characterizing canonical metrics on Hermitian locally symmetric manifolds X of non-compact/compact types in terms of curvature conditions. The proofs of these metric rigidity theorems are applied to the study of holomorphic mappings between manifolds X of the same type. Moreover, a dual version of the generalized Frankel Conjecture on characterizing compact Kähler manifolds are also formulated.
Contents:
- Background and First Results: Historical Background and Summary of
Results
- Fundamentals of Hermitian and Kähler Geometries
- Riemannian and Hermitian Symmetric Manifolds
- Bounded Symmetric Domains – the Classical Cases
- Bounded Symmetric Domains – General Theory
- The Hermitian Metric Rigidity Theorem for Compact Quotients
- The Kähler Metric Rigidity Theorem in the Semipositive Case
- Further Development: The Hermitian Metric Rigidity Theorem for Quotients of Finite Volume
- The Immersion Problem for Complex Hyperbolic Space Forms
- The Hermitian Metric Rigidity Theorem on Locally Homogeneous Holomorphic Vector Bundles
- A Rigidity Theorem for Holomorphic Mappings between Irreducible Hermitian Symmetric Manifolds of Compact Type
- Appendix: Semisimple Lie Algebras and Their Representations
- Some Theorems in Riemannian Geometry
- Characteristic Projective Subvarieties Associated to Hermitian Symmetric Manifolds
- A Dual Generalized Frankel Conjecture for Compact Kähler Manifolds of Seminegative Bisectional Curvature
Readership: Mathematicians.
| 292pp |
Pub. date: Jul 1989 |
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