Related papers: Sasaki-Einstein Manifolds
This article presents a novel mathematical formalism for advanced manifold--metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional…
We present a new construction for obtaining pairs of higher-step isospectral Riemannian nilmanifolds and compare several resulting new examples. In particular, we present new examples of manifolds that are isospectral on functions, but not…
Warped embeddings from a lower dimensional Einstein manifold into a higher dimensional one are analyzed. Explicit solutions for the embedding metrics are obtained for all cases of codimension 1 embeddings and some of the codimension n>1…
Improper affine spheres have played an important role in the development of geometric methods for the study of the Hessian one equation. Here, we review most of the advances we have made in this direction during the last twenty years.
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…
This is a survey on special metrics. We shall present some results and open questions on special metrics mainly appeared in the last 10 years
In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts…
This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview of recent methods and results in "Blaschkean integral…
The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenb\"ock formulas for the…
This is a survey of recent results on manifolds with positive curvature from a series of lecture given in Guanajuato, Mexico in 2010. It also contains some hitsorical comments.
A simplified, user-friendly repackaging of the curvature estimates implied by the Seiberg-Witten equations is formulated in terms of the convex hull of the set of monopole classes. New results are also obtained concerning boundary cases of…
The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…
We survey the progress on the study of symplectic geometry past five decades. The survey focuses on the convexity properties of a moment map, the classification of symplectic actions, the symplectic embedding problems, and the theory of…
A new topological invariant of closed connected orientable four-dimensional manifolds is proposed. The invariant, constructed via surgery on a special link, is a four-dimensional counterpart of the celebrated SU(2) three-manifold invariant…
We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point of the generalized almost contact…
The classification of the possible equilibrium shapes that a self-gravitating fluid can take in a Riemannian manifold is a classical problem in mathematical physics. In this paper it is proved that the equilibrium shapes are isoparametric…
Associated to any supermanifold is a filtration by spaces, referred to as thickenings. It is the objective of this article to study them up to a certain equivalence and then up to isomorphism in the complex-analytic setting. We study them…
We study the deformation theory of projective Stanley-Reisner schemes associated to combinatorial manifolds. We achieve detailed descriptions of first order deformations and obstruction spaces. Versal base spaces are given for certain…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…