In this paper, we classified the paracontact metric κ,μ-manifold satisfying the Miao-Tam critical equation with κ>−1. We proved that it is locally isometric to the product of a flat n+1-dimensional ...manifold and an n-dimensional manifold of negative constant curvature −4.
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This volume contains the proceedings of the conference on tropical geometry and integrable systems, held July 3-8, 2011, at the University of Glasgow, United Kingdom. One of the aims of this ...conference was to bring together researchers in the field of tropical geometry and its applications, from apparently disparate ends of the spectrum, to foster a mutual understanding and establish a common language which will encourage further developments of the area. This aim is reflected in these articles, which cover areas from automata, through cluster algebras, to enumerative geometry. In addition, two survey articles are included which introduce ideas from researchers on one end of this spectrum to researchers on the other. This book is intended for graduate students and researchers interested in tropical geometry and integrable systems and the developing links between these two areas.
The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many ...important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.
We revisit the famous Buffon’s needle problem, one of the first problems in geometric probability. Only now, the plane upon which we toss our needles is not Euclidean, as it was for Buffon, but ...instead has the simple but fascinating taxicab geometry. We find that we get the exact same solution as Buffon did, except that now π = 4! As a bonus, we get nice introductions to basic probability theory and geometry.
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This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12-15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's ...60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.
Using Dwork's theory, the authors prove a broad generalization of his famous p-adic formal congruences theorem. This enables them to prove certain p-adic congruences for the generalized ...hypergeometric series with rational parameters; in particular, they hold for any prime number p and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the "Eisenstein constant" of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement "on average" of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.
This book provides a comprehensive introduction into the classical topic of projective geometry. It explains how metric concepts may be best understood in projective terms and explores the beauty of ...the interplay of geometry, algebra and combinatorics.
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30.
The ambient metric Fefferman, Charles; Graham, C. Robin
2012., 20111114, 2011, 2012-01-01, Volume:
178
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This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient ...metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics.
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