oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
Piecewise linear manifolds: Einstein metrics and Ricci flows  [PDF]
Robert Schrader
Mathematics , 2015,
Abstract: This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given set of piecewise linear spaces we define and discuss (normalized) Ricci flows. Piecewise linear Einstein metrics are defined and examples are provided. Criteria for flows to approach Einstein metrics are formulated. Second variations of the total scalar curvature at a specific Einstein space are calculated.
Curvature-homogeneous indefinite Einstein metrics in dimension four: the diagonalizable case  [PDF]
Andrzej Derdzinski
Mathematics , 2002,
Abstract: We classify those curvature-homogeneous Einstein four-manifolds, of all metric signatures, which have a complex-diagonalizable curvature operator. They all turn out to be locally homogeneous. More precisely, any such manifold must be either locally symmetric or locally isometric to a suitable Lie group with a left-invariant metric. To show this we explicitly determine the possible local-isometry types of manifolds that have the properties named above, but are not locally symmetric.
Convergence Results for Two Kahler-Ricci Flows  [PDF]
Zhou Zhang
Mathematics , 2013,
Abstract: In this note, we provide some general discussion on the two main versions in the study of Kahler-Ricci flows over closed manifolds, aiming at smooth convergence to the corresponding Kahler-Einstein metrics with assumptions on the volume form and Ricci curvature form along the flow.
Moduli spaces of critical Riemannian metrics in dimension four  [PDF]
Jeff Viaclovsky,Gang Tian
Mathematics , 2003,
Abstract: We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With certain geometric assumptions, the moduli space can be compactified by adding metrics with orbifold singularities. Similar results were obtained previously for Einstein metrics, but our analysis differs substantially from the Einstein case in that we do not assume any pointwise Ricci curvature bound.
Metrics of Special Curvature with Symmetry  [PDF]
Brandon Dammerman
Mathematics , 2006,
Abstract: Various curvature conditions are studied on metrics admitting a symmetry group. We begin by examining a method of diagonalizing cohomogeneity-one Einstein manifolds and determine when this method can and cannot be used. Examples, including the well-known Stenzel metrics, are discussed. Next, we present a simplification of the Einstein condition on a compact four manifold with $T^{2}$-isometry to a system of second-order elliptic equations in two-variables with well-defined boundary conditions. We then study the Einstein and extremal Kahler conditions on Kahler toric manifolds. After constructing explicitly new extremal Kahler and constant scalar curvature metrics, we demonstrate how these metrics can be obtained by continuously deforming the Fubini-Study metric on complex projective space in dimension three. We also define a generalization of Kahler toric manifolds, which we call fiberwise Kahler toric manifolds, and construct new explicit extremal Kahler and constant scalar curvature metrics on both compact and non-compact manifolds in all even dimensions. We also calculate the Futaki invariant on manifolds of this type. After describing an Hermitian non-Kahler analogue to fiberwise Kahler toric geometry, we construct constant scalar curvature Hermitian metrics with $J$-invariant Riemannian tensor. In dimension four, we write down explicitly new constant scalar curvature Hermitian metrics with $J$-invariant Ricci tensor. Finally, we integrate the scalar curvature equation on a large class of cohomogeneity-one metrics.
Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes  [PDF]
Daniel Champion,Andrew Marchese,Jacob Miller,Andrea Young
Mathematics , 2010,
Abstract: In [7], a notion of constant scalar curvature metrics on piecewise flat manifolds is defined. Such metrics are candidates for canonical metrics on discrete manifolds. In this paper, we define a class of vertex transitive metrics on certain triangulations of $\mathbb{S}^3$; namely, the boundary complexes of cyclic polytopes. We use combinatorial properties of cyclic polytopes to show that, for any number of vertices, these metrics have constant scalar curvature.
The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature
Enli Guo,Xiaohuan Mo,Xianqiang Zhang
Symmetry, Integrability and Geometry : Methods and Applications , 2009,
Abstract: By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.
The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature  [PDF]
Enli Guo,Xiaohuan Mo,Xianqiang Zhang
Mathematics , 2009, DOI: 10.3842/SIGMA.2009.045
Abstract: By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.
On the curvature of invariant Kropina metrics  [PDF]
H. R. Salimi Moghaddam
Mathematics , 2013,
Abstract: In the present article we compute the flag curvature of a special type of invariant Kropina metrics on homogeneous spaces.
Metrics of positive scalar curvature and unbounded widths  [PDF]
Rafael Montezuma
Mathematics , 2015,
Abstract: In this work we construct a sequence of Riemannian metrics on the three-sphere with scalar curvature greater than or equal to $6$ and arbitrarily large widths. Our procedure is based on the connected sum construction of positive scalar curvature metrics due to Gromov and Lawson. We develop analogies between the area of boundaries of special open subsets in our three-manifolds and $2$-colorings of associated full binary trees. Then, via combinatorial arguments and using the relative isoperimetric inequality, we argue that the widths converge to infinity.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.