Results 1 to 10 of about 16,847 (81)

Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds [PDF]

Colloquium Mathematicum, 2022
Summary: We study rigidity of critical metrics for quadratic curvature functions \(\mathcal{F}_{t,s}(g)\) involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor. In particular, when \(s=0\), we give new characterizations by pointwise inequalities involving the Weyl curvature and the traceless Ricci tensor for critical ...
Ma, Bingqing, Huang, Guangyue
openaire   +2 more sources

Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds

Advances in Mathematics, 2007
We consider the moduli space of the extremal K hler metrics on compact manifolds. We show that under the conditions of two-sided total volume bounds, $L^{n\over2}$-norm bounds on $\Riem$, and Sobolev constant bounds, this Moduli space can be compactified by including (reduced) orbifolds with finitely many singularities.
Chen, Xiuxiong, Weber, Brian
  +5 more sources

Some rigidity results on critical metrics for quadratic functionals [PDF]

, 2014
In this paper we prove rigidity results on critical metrics for quadratic curvature functionals, involving the Ricci and the scalar curvature, on the space of Riemannian metrics with unit volume. It is well-known that Einstein metrics are always critical
Catino, Giovanni
core   +2 more sources

Geometric thermodynamics: black holes and the meaning of the scalar curvature [PDF]

, 2014
In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions ...
del Castillo, Gerardo F. Torres, García-Ariza, Miguel Á., Montesinos, Merced   +2 more
core   +2 more sources

Generalized Cylinders in Semi-Riemannian and Spin Geometry [PDF]

, 2003
We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into
Andrei Moroianu, Bourguignon, Bär, Christian B�r, Friedrich, Mounoud, Paul Gauduchon   +6 more
core   +5 more sources

A spinorial energy functional: critical points and gradient flow [PDF]

, 2015
On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor {\phi}.
A Besse, A Fischer, A Gray, A Moroianu, B Ammann, B McInnes, Bernd Ammann, C Bär, C Bär, D Conti, D DeTurck, D Joyce, F Pfäffle, Frederik Witt, H Baum, H Lawson, H Weiß, H Weiß, Hartmut Weiss, J Cheeger, J Kazdan, J Nordström, J-P Bourguignon, M Fernández, M Taylor, M Wang, M Wang, M Wang, N Hitchin, O Ladyzhenskaya, P Topping, R Goto, ST Yau, T Aubin, T Friedrich, T Friedrich, T Friedrich, T Friedrich, X Dai, Y Kosmann   +39 more
core   +2 more sources

On Gauss-Bonnet Curvatures [PDF]

, 2007
The $(2k)$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k)$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k=1$.
Labbi, Mohammed Larbi
core   +4 more sources

Critical metrics for Riemannian curvature functionals [PDF]

, 2016
78 pages, 1 ...
openaire   +2 more sources

Moduli spaces of critical Riemannian metrics in dimension four

Advances in Mathematics, 2005
24 pages, to appear in Advances in ...
Tian, Gang, Viaclovsky, Jeff
openaire   +2 more sources

Information-Geometric Models in Data Analysis and Physics

Mathematics
Information geometry provides a data-informed geometric lens for understanding data or physical systems, treating data or physical states as points on statistical manifolds endowed with information metrics, such as the Fisher information.
D. Bernal-Casas, José M. Oller
doaj   +1 more source