The Global Sections of Chiral de Rham Complexes on Compact Ricci-Flat Kähler Manifolds

Triangular De Rham Cohomology of Compact Kähler Manifolds

We study the de Rham 1-cohomology H 1 DR (M, G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principal bundle M × G by the so-called gauge equivalence. We consider the case when M is a compact Kähler manifold and G is a solvable complex linear algebraic group of a special class which contains the Borel sub...

Ricci flow on compact Kähler manifolds of positive bisectional

where ω̃ = ( √ −1/2)g̃ij̄dz ∧ dz and Σ̃ = ( √ −1/2)R̃ij̄dz ∧ dz are the Kähler form, the Ricci form of the metric g̃ respectively, while c1(M) denotes the first Chern class. Under the normalized initial condition (2), the first author [3] (see also Proposition 1.1 in [4]) showed that the solution g(x, t) = ∑ gij̄(x, t)dz dz to the normalized flow (1) exists for all time. Furthermore by the work of Mok ...

The Structure of Compact Ricci-flat Riemannian Manifolds

where k is the first Betti number b^M), T is a flat riemannian λ -torus, M~ is a compact connected Ricci-flat (n — λ;)-manifold, and Ψ is a finite group of fixed point free isometries of T x M' of a certain sort (Theorem 4.1). This extends Calabi's result on the structure of compact euclidean space forms ([7] see [20, p. 125]) from flat manifolds to Ricci-flat manifolds. We use it to essentiall...

0 Ricci flow on Kähler manifolds

Ricci Flow on Kähler-einstein Manifolds