Moduli spaces of Einstein metrics

نویسنده

  • Heather Macbeth
چکیده

We discuss the space of Einstein metrics, up to diffeomorphism, on a compact manifold. In particular we mention some heuristics on its dimension and some theorems on its compactness.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On quasi-Einstein Finsler spaces‎

‎The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces‎. ‎Quasi-Einstein metrics serve also as solution to the Ricci flow equation‎. ‎Here‎, ‎the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined‎. ‎In compact case‎, ‎it is proved that the quasi-Einstein met...

متن کامل

Curvature and Injectivity Radius Estimates for Einstein 4-manifolds

It is of fundamental interest to study the geometric and analytic properties of compact Einstein manifolds and their moduli. In dimension 2 these problems are well understood. A 2-dimensional Einstein manifold, (M, g), has constant curvature, which after normalization, can be taken to be −1, 0 or 1. Thus, (M, g) is the quotient of a space form and the metric, g, is completely determined by the ...

متن کامل

Moduli Spaces of Einstein Metrics on 4-manifolds

In this note, we announce some results showing unexpected similarities between the moduli spaces of constant curvature metrics on 2-manifolds (the Riemann moduli space) and moduli spaces of Einstein metrics on 4manifolds. Let J? denote the moduli space of Einstein metrics of volume 1 on a compact, orientable 4-manifold M. If J£\ denotes the space of smooth Riemannian metrics of volume 1 on M, e...

متن کامل

Positivity of Relative Canonical Bundles of Families of Canonically Polarized Manifolds

The Kähler-Einstein metrics on the fibers of an effectively parameterized family of canonically polarized manifolds induce a hermitian metric on the relative canonical bundle. We use a global elliptic equation to show that this metric is strictly positive. Applications concern the curvature of the classical and generalized Weil-Petersson metrics and hyperbolicity of moduli spaces.

متن کامل

Weil-petersson Geometry on Moduli Space of Polarized Calabi-yau Manifolds

Moduli spaces of general polarized algebraic varieties are studied extensively by algebraic geometers. However, there are two classes of moduli spaces where the methods of differential geometry are equally powerful. These are the moduli spaces of curves and the moduli spaces of polarized Calabi-Yau manifolds. Both spaces are complex orbifolds. The Weil-Petersson metric is the main tool for inve...

متن کامل

ذخیره 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 2011