Study Ricci flow on CP1-bundles over Kähler-Einstein manifolds.
problem Preserving an initial metric on CP1-bundles.
method Ricci flow on CP1-bundles over a product of Kähler-Einstein manifolds.
result The ansatz is preserved along the Ricci flow.
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13 results for “CP1”
We describe the connected components of the complement of a natural "diagonal" of real codimension 1 in a stratum of quadratic differentials on CP1. We establish a natural bijection between the set of these connected components and the set of generic configurations that appear on such "flat spheres". We also prove that…
Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle whose total space Z admits a natural metric h. The aim of this article is to study properties of complex structures on (Z,h) which are compatible with the CP1-fibration and the metric h. The results obtained enable us to translate some metric …
The paper finds infinite pairs of CP1-structures sharing same holonomy.
problem Finding pairs of CP1-structures with same holonomy.
method Analyzes marked Riemann surfaces and their CP1-structures.
result There are exactly countably infinite pairs of CP1-structures sharing holonomy.
Let (X,L) be a polarized Kähler manifold that admits an extremal Kähler metric in c1(L). We show that on a nearby polarized deformation that preserves the symmetry induced by the extremal vector field of (X,L), the modified K-energy is bounded from below. This generalizes a result of Chen, Székelyhidi and Tosatti to ex…
Local tri-Hamiltonian structure for Ablowitz-Ladik hierarchy established.
problem Establishing a tri-Hamiltonian structure for the Ablowitz-Ladik hierarchy.
method Constructing a local tri-Hamiltonian structure and computing central invariants.
result Central invariants of one bi-Hamiltonian structure are 1/24, and dispersionless limit matches Frobenius manifold.
In this paper we investigate flows on discrete curves in $\C^2$, $\CP^1$, and $\C$. A novel interpretation of the one dimensional Toda lattice hierarchy and reductions thereof as flows on discrete curves will be given.
The paper studies neck-pinching of CP1-structures on surfaces, describing their limits.
problem Characterizing the degeneration of -structures on surfaces.
method Analyzing a path of -structures leaving every compact subset, converging holonomy in the PSL(2, C)-character variety.
result The limit of the path is described in terms of developing maps, holomorphic quadratic differentials, and pleated surfaces.
Study Higgs bundles on CP1 with specific singularities, linking fixed points to W-algebra representations.
problem Analyzing Higgs bundles with irregular singularities and their fixed points.
method Introduced a -action on and classified its fixed points.
result Found a 1-1 correspondence between fixed points and certain W-algebra representations.
Configurations of rigid collections of saddle connections are connected component invariants for strata of the moduli space of quadratic differentials. They have been classified for strata of Abelian differentials by Eskin, Masur and Zorich. Similar work for strata of quadratic differentials has been done in Masur and …
New insights into a complex hyperbolic braid group quotient.
problem Understanding a complex hyperbolic braid group quotient.
method Analyzing the moduli space of 12-tuples in CP1 and identifying loops.
result Identifying loops in the 9-ball quotient corresponding to standard braid generators.
New Einstein metrics constructed on complex line bundle over CP1.
problem Constructing -invariant negative Einstein metrics on complex line bundles.
method Rigorous numerics to approximate, then fixed-point methods to perturb to genuine Einstein metrics.
result Complete, asymptotically hyperbolic Einstein metrics constructed.
We present an explicit algorithm for tessellating the algebraic surfaces (real 4-manifolds) F(n) embedded in CP3 defined by the equation z0^n + z1^n + z2^n + z3^n = 0 in the standard homogeneous coordinates [z0, z1, z2, z3], where n is any positive integer. Note that F(4) in particular is a K3 surface. Our tessellation…