Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAn Integrability Theorem for Almost-Kahler Structures using J-anti-invariant Two-Forms on Four-Manifolds
167
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We establish a new criterion for a compatible almost complex structure on a symplectic four-manifold to be integrable and hence Kahler. Our main theorem shows that the existence of three linearly independent closed J-anti-invariant two-forms implies the integrability of the almost complex structure. This proves the conjecture of Draghici-Li-Zhang in the almost-Kahler case
rate research
Read More
We find a new class of invariant metrics existing on the tangent bundle of any given almost-Hermitian manifold. We focus here on the case of Riemannian surfaces, which yield new examples of Kahlerian Ricci-flat manifolds in four real dimensions.
We find a family of Kahler metrics invariantly defined on the radius $r_0>0$ tangent disk bundle ${{cal T}_{M,r_0}}$ of any given real space-form $M$ or any of its quotients by discrete groups of isometries. Such metrics are complete in the non-negative curvature case and non-complete in the negative curvature case. If $dim M=2$ and $M$ has constant sectional curvature $K eq0$, then the Kahler manifolds ${{cal T}_{M,r_0}}$ have holonomy $mathrm{SU}(2)$; hence they are Ricci-flat. For $M=S^2$, just this dimension, the metric coincides with the Stenzel metric on the tangent manifold ${{cal T}_{S^2}}$, giving us a new most natural description of this well-know metric.
In this paper, we prove a Liouville theorem for holomorphic functions on a class of complete Gauduchon manifolds. This generalizes a result of Yau for complete Kahler manifolds to the complete non-Kahler case.
We define flag structures on a real three manifold M as the choice of two complex lines on the complexified tangent space at each point of M. We suppose that the plane field defined by the complex lines is a contact plane and construct an adapted connection on an appropriate principal bundle. This includes path geometries and CR structures as special cases. We prove that the null curvature models are given by totally real submanifolds in the flag space SL(3, C)/B, where B is the subgroup of upper triangular matrices. We also define a global invariant which is analogous to the Chern-Simons secondary class invariant for three manifolds with a Riemannian structure and to the Burns-Epstein invariant in the case of CR structures. It turns out to be constant on homotopy classes of totally real immersions in flag space.
In this paper, we develop holomorphic Jacobi structures. Holomorphic Jacobi manifolds are in one-to-one correspondence with certain homogeneous holomorphic Poisson manifolds. Furthermore, holomorphic Poisson manifolds can be looked at as special cases of holomorphic Jacobi manifolds. We show that holomorphic Jacobi structures yield a much richer framework than that of holomorphic Poisson structures. We also discuss the relationship between holomorphic Jacobi structures, generalized contact bundles and Jacobi-Nijenhuis structures.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
