Journal ArticleDOI
On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
Reads0
Chats0
TLDR
In this paper, the Ricci form of some Kahler metric is shown to be closed and its cohomology class must represent the first Chern class of M. This conjecture of Calabi can be reduced to a problem in non-linear partial differential equation.Abstract:
Therefore a necessary condition for a (1,l) form ( G I a ' r r ) I,,, Rlr dz' A d? to be the Ricci form of some Kahler metric is that it must be closed and its cohomology class must represent the first Chern class of M. More than twenty years ago, E. Calabi [3] conjectured that the above necessary condition is in fact sufficient. This conjecture of Calabi can be reduced to a problem in non-linear partial differential equation.read more
Citations
More filters
Journal ArticleDOI
Gravitation, Gauge Theories and Differential Geometry
TL;DR: In this article, the Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, Illinois, USA Peter B. GILKEY Fine Hall, Box 37.
Journal ArticleDOI
On the existence of hermitian‐yang‐mills connections in stable vector bundles
Karen Uhlenbeck,Shing-Tung Yau +1 more
Journal ArticleDOI
Kähler-Einstein metrics with positive scalar curvature
TL;DR: In this article, it was shown that the existence of Kahler-Einstein metrics implies the stability of the underlying Kahler manifold in a suitable sense, which disproves a long-standing conjecture that a compact KG admits KG metrics if it has positive first Chern class and no nontrivial holomorphic vector fields.
Journal ArticleDOI
Comments on Conifolds
Philip Candelas,Xenia de la Ossa +1 more
TL;DR: In this paper, the Ricci-flat Kahler metric is calculated in the vicinity of the nodes for the conifold, the resolution and the deformation, and it is shown that, owing to a topological obstruction, the manifold obtained as the result of independently resolving and deforming the nodes of a conifolds in general cannot be Kahler.
Journal ArticleDOI
The Geometry of String Perturbation Theory
Eric D'Hoker,Duong H. Phong +1 more
TL;DR: In this paper, recent progress made towards the understanding of closed bosonic and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean space-time, is devoted to recent progress.
References
More filters
Book
Geometric Measure Theory
TL;DR: In this article, Grassmann algebras of a vectorspace have been studied in the context of the calculus of variations, and a glossary of some standard notations has been provided.
BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.
Journal ArticleDOI
Calabi's conjecture and some new results in algebraic geometry
TL;DR: A proof of Calabi's conjectures on the Ricci curvature of a compact Kähler manifold is announced and some new results in algebraic geometry and differential geometry are proved, including that the only Köhler structure on a complex projective space is the standard one.