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Ricci surfaces
minimal surfaces Ricci condition generalized Killing spinors Ricci surfaces
2012/6/29
A Ricci surface is a Riemannian 2-manifold $(M,g)$ whose Gaussian curvature $K$ satisfies $K\Delta K+g(dK,dK)+4K^3=0$. Every minimal surface isometrically embedded in $\mathbb{R}^3$ is a Ricci surface...
On complete constant mean curvature vertical multigraphs in E(κ,τ)
multigraphs constant mean curvature homogeneous spaces
2012/6/29
We prove that any complete surface with constant mean curvature in a homogeneous space E(\kappa,\tau) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a cons...
Eigenvalues control for a Finsler--Laplace operator
Eigenvalues control Finsler--Laplace operator Differential Geometry
2012/6/27
Using the definition of a Finsler--Laplacian given by the first author, we show that two bi-Lipschitz Finsler metrics have a controlled spectrum. We deduce from that several generalizations of Riemann...
Let F be a Riemannian submersion from an almost Hermitian manifold (M; gM; J) onto a Riemannian manifold (N; gN). We introduce the notion of the v-semi-slant submersion. And then we obtain some proper...
Equidistant hypersurfaces of the bidisk
Equidistant hypersurfaces the bidisk Differential Geometry
2012/6/25
The following are notes on the geometry of the bidisk. In particular, we examine the properties of equidistant surfaces in the bidisk.
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...
On the classification of homogeneous Einstein metrics on generalized flag manifolds with $b_2(M)=1$
Homogeneous Einstein metric flag manifold second Betti number finiteness conjecture twistor fibration
2012/6/25
We study homogeneous Einstein metrics for a class of compact homogeneous spaces, namely generalized flag manifolds $G/H$ with second Betti number $b_{2}(G/H)=1$. There are 33 such manifolds which have...
Einstein metrics and Yamabe invariants of weighted projective spaces
Einstein metrics Yamabe invariants weighted projective spaces Differential Geometry
2012/6/25
An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe in...
We characterize helix surfaces in the Berger sphere. In particular, we prove that, locally, a helix surface is invariant by the action of a 1-parameter group of isometries of the ambient space.
Geometry of optimal control for control-affine systems
affine distributions optimal control theory Cartan's method of equivalence
2012/6/21
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We comput...
Hodge cohomology of iterated fibred cusp metrics on Witt spaces
Hodge cohomology iterated fibred cusp metrics Witt spaces Differential Geometry
2012/6/21
On a Witt space, we identify the $L^2$ cohomology of iterated fibred cusp metrics with the middle perversity intersection cohomology of the corresponding stratified space.
There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions $n$...
In this paper, we use Pacard-Xu's methods to discuss the complex deformation of constant scalar curvature metrics in the case of fixed and varying complex structures. Moreover, we also discuss the com...
Difference bodies in complex vector spaces
Difference bodies complex vector spaces Differential Geometry
2012/6/21
A complete classification is obtained of continuous, translation invariant, Minkowski valuations on an m-dimensional complex vector space which are covariant under the complex special linear group.
The Yamabe constant on noncompact manifolds
The Yamabe constant noncompact manifolds Differential Geometry
2012/6/19
We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the ...