Uniformization of four manifolds
نویسنده
چکیده
We characterize those Einstein four manifolds which are locally symmetric spaces of noncompact type. Namely they are four manifolds which admit solutions to the (non-Abelian) Seiberg Witten equations and satisfy certain characteristic number equality.
منابع مشابه
Classification of Bochner Flat Kähler Manifolds by Heisenberg, Spherical CR Geometry
A Bochner flat Kähler manifold is a Kähler manifold with vanishing Bochner curvature tensor. We shall give a uniformization of Bochner flat Kähler manifolds. One of the aims of this paper is to give a correction to the proof of our previous paper [9] concerning uniformization of Bochner flat Kähler manifolds. A Bochner flat locally conformal Kähler manifold is a locally conformal Kähler manifol...
متن کاملGradient Kähler-ricci Solitons and a Uniformization Conjecture
In this article we study the limiting behavior of the KählerRicci flow on complete non-compact Kähler manifolds. We provide sufficient conditions under which a complete non-compact gradient KählerRicci soliton is biholomorphic to C. We also discuss the uniformization conjecture by Yau [15] for complete non-compact Kähler manifolds with positive holomorphic bisectional curvature.
متن کاملYang-mills Flow and Uniformization Theorems
We consider a parabolic-like systems of differential equations involving geometrical quantities to examine uniformization theorems for twoand three-dimensional closed orientable manifolds. We find that in the two-dimensional case there is a simple gauge theoretic flow for a connection built from a Riemannian structure, and that the convergence of the flow to the fixed points is consistent with ...
متن کاملOn Lorentzian two-Symmetric Manifolds of Dimension-four
‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎.
متن کاملMiyaoka-yau Type Inequalities for Kähler-einstein Manifolds
We investigate Chern number inequalities on Kähler-Einstein manifolds and their relation to uniformization. For Kähler-Einstein manifolds with c1 > 0, we prove certain Chern number inequalities in the toric case. For Kähler-Einstein manifolds with c1 < 0, we propose a series of Chern number inequalities, interpolating Yau’s and Miyaoka’s inequalities.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997