Weyl Curvature and the Euler Characteristic in Dimension Four
نویسنده
چکیده
We give lower bounds, in terms of the Euler characteristic, for the L-norm of the Weyl curvature of closed Riemannian 4-manifolds. The same bounds were obtained by Gursky, in the case of positive scalar curvature metrics.
منابع مشابه
Conformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
متن کاملOn Special Generalized Douglas-Weyl Metrics
In this paper, we study a special class of generalized Douglas-Weyl metrics whose Douglas curvature is constant along any Finslerian geodesic. We prove that for every Landsberg metric in this class of Finsler metrics, ? = 0 if and only if H = 0. Then we show that every Finsler metric of non-zero isotropic flag curvature in this class of metrics is a Riemannian if and only if ? = 0.
متن کاملar X iv : g r - qc / 0 20 20 81 v 1 2 1 Fe b 20 02 The non - existence of a Lanczos potential for the Weyl curvature tensor in dimensions n ≥ 7
In this paper it is shown that a Lanczos potential for the Weyl curvature tensor does not exist for all spaces of dimension n ≥ 7. Whether there exists a Lanczos potential [1] for Weyl curvature tensors in dimensions n > 4 has still not been determined. Although Lanczos's original proof [1] for existence was flawed [2], there have subsequently been complete proofs for existence in four dimensio...
متن کاملCharacteristic Length and Clustering
We explore relations between various variational problems for graphs: among the functionals considered are Euler characteristic χ(G), characteristic length μ(G), mean clustering ν(G), inductive dimension ι(G), edge density (G), scale measure σ(G), Hilbert action η(G) and spectral complexity ξ(G). A new insight in this note is that the local cluster coefficient C(x) in a finite simple graph can ...
متن کاملA graph theoretical Gauss-Bonnet-Chern Theorem
We prove a discrete Gauss-Bonnet-Chern theorem ∑ g∈V K(g) = χ(G) for finite graphs G = (V,E), where V is the vertex set and E is the edge set of the graph. The dimension of the graph, the local curvature form K and the Euler characteristic are all defined graph theoretically.
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 2005