Related papers: Sasaki-Einstein Manifolds
I review some aspects of supersymmetric grand unification and emphasize a recent development in the area of gauge coupling unification.
In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of…
We provide a new, self-contained and more conceptual proof of the result that an almost contact metric manifold of dimension greater than 5 is Sasakian if and only if it is nearly Sasakian.
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an…
This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical,…
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
In this paper, we prove an existence theorem of a local moduli space for geometric structures in a very general setting. Then to show the interest of this result, we apply it to the case of sasakian and Sasaki-Einstein structures.
Holomorphic manifolds over Cayley-Dickson algebras are defined and their embeddings and immersions are studied.
In this article, we consider Einstein-type manifolds with boundary which generalizes important geometric equations, like static vacuum and static perfect fluid. We investigate some geometric inequalities for those manifolds. Then, we…
This is a sequel to the survey given by the author in Surveys in Differential Geometry Vol. 6 in 1999. The present survey covers selected developments since 1999 to 2011 dealing with the construction of Einstein metrics on bundles and…
We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove…
We show that #8(S^2 times S^3) admits two 8-dimensional complex families of inequivalent non-regular Sasakian-Einstein structures. These are the first known non-regular Sasakian-Einstein metrics on this 5-manifold.
We begin with a brief discussion of the building blocks of supersymmetric grand unified theories. We recall some of the compelling theoretical reasons for viewing supersymmetric grand unification as an attractive avenue for physics beyond…
We review basic facts on the structure of nearly K\"ahler manifolds, focussing in particular on the six-dimensional case. A self-contained proof that nearly K\"ahler six-manifolds are Einstein is given by combining different known results.…
This is an expository article. Among other topics, we discuss the existence of Kahler-Ricci soliton metrics on toric Fano manifolds, and Kahler-Einstein metrics on deformations of the Mukai-Umemura 3-fold
This paper is a survey on the structure of manifolds with a lower Ricci curvature bound.
This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…