منابع مشابه
PRESCRIBING SCALAR CURVATURE ON Sn
on S for n ≥ 3. In the case R is rotationally symmetric, the well-known Kazdan-Warner condition implies that a necessary condition for (1) to have a solution is: R > 0 somewhere and R′(r) changes signs. Then, (a) is this a sufficient condition? (b) If not, what are the necessary and sufficient conditions? These have been open problems for decades. In Chen & Li, 1995, we gave question (a) a nega...
متن کاملOn the Scalar Curvature of Einstein Manifolds
We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse [6, p. 19]. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.
متن کاملThe Scalar Curvature Equation on S 3
An obvious necessary condition for the existence of solutions to (1.1) is that the function K has to be positive somewhere. Moreover, there are the Kazdan-Warner obstructions [7, 16], which imply in particular, that a monotone function of the coordinate function X1 cannot be realized as the scalar curvature of a metric conformal to g0. Numerous studies have been made on equation (1.1) and its h...
متن کاملScalar Curvature Fluctuations on the Four–Sphere
Two-point functions of the scalar curvature for metric fluctuations on the four–sphere are analysed. The two-point function for points separated by a fixed distance and for metrics of fixed volume is calculated using spacetime foam methods. This result can be used for comparison between the continuum approach to quantum gravity and numerical quantum gravity on the lattice. Pacs numbers: 03.70.+...
متن کاملOn the Scalar Curvature of Complex Surfaces
Let (M, J) be a minimal compact complex surface of Kähler type. It is shown that the smooth 4-manifold M admits a Riemannian metric of positive scalar curvature iff (M,J) admits a Kähler metric of positive scalar curvature. This extends previous results of Witten and Kronheimer. A complex surface is a pair (M,J) consisting of a smooth compact 4-manifold M and a complex structure J on M ; the la...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2010
ISSN: 0022-040X
DOI: 10.4310/jdg/1271271793