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We introduce the notion of recurrent geodesic rays in
a complete °at Lorentz 3-manifold. We completely classify the
dynamical behavior of geodesics in cyclic quotients, and apply this
classiˉcation...
Convergence of scalar-flat metrics on manifolds with boundary under the Yamabe flow
Convergence of scalar-flat metrics manifolds boundary under the Yamabe flow Differential Geometry
2012/6/21
This paper is concerned with a Yamabe-type flow for compact Riemannian manifolds with boundary. The convergence of this flow is established if the manifold with boundary satisfies either a generic con...
Frobenius 3-folds via singular flat 3-webs
Frobenius 3-folds singular flat 3-webs Differential Geometry
2012/6/15
We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ sa...
Bach-flat gradient steady Ricci solitons
Bach-flat gradient Ricci solitons Differential Geometry
2011/9/19
Abstract: In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci solitons with positive Ricci curvature is isometric to the Bryant soliton. We also show th...
Mass-capacity inequalities for conformally flat manifolds with boundary
Mass-capacity inequalities conformally flat manifolds boundary
2011/8/29
Abstract: In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, capacity and Ale...
Flat Pseudo-Riemannian Homogeneous Spaces with Non-Abelian Holonomy Group
Flat Pseudo-Riemannian Homogeneous Spaces Non-Abelian Holonomy Group
2010/12/8
We construct homogeneous flat pseudo-Riemannian manifolds with non-abelian fundamental group. In the compact case, all homogeneous flat pseudo-Riemannian manifolds are complete and have abelian linear...
ON CONFORMALLY FLAT LORENTZIAN SPACES SATISFYING A CERTAIN CONDITION ON THE CURVATURE TENSOR
CONFORMALLY FLAT LORENTZIAN SPACES CURVATURE TENSOR
2010/3/17
In this paper we prove a local classification theorem for the conformally flat lorentzian spaces satisfying the condition R(X,Y)R=0.