The ambient metric Fefferman, Charles; Graham, C. Robin
2012., 20111114, 2011, 2012-01-01, Volume:
178
eBook
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.
In this paper, we study hypersurfaces of the homogeneous nearly Kähler manifold S 3 ×S 3 with typical properties. We first show that in the NK S 3 ×S 3 there exist neither totally umbilical ...hypersurfaces nor hypersurfaces of parallel second fundamental form. Then we investigate hypersurfaces of S 3 ×S 3 such that its shape operator A and induced almost contact structure satisfy the condition A = A, and as the main result, a complete classification of this remarkable family of hypersurfaces in S 3 ×S 3 is presented.
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Time-varying Mesh Stiffness (TVMS) is one of the important parameter variables in the study of gear system dynamics. It is crucial to accurately simulate TVMS for the analysis of dynamic performance ...response indexes of gear transmission system such as vibration and noise. On the basis of meshing kinematic equation and geometric position relation of involute gear，one accurate modeling method of spur gear pairs based on geometry and potential energy method is proposed. The meshing limit boundary conditions of standard involute profile is analyzed in real-time and effectively，and a computational analysis model of TVMS from physical model to mathematical model is constructed which combined with the potential energy method. The TVMS of spur gear pair is calculated accurately by numerical calculation method，and an example is given to illustrate its application. On the allowable range of bearing capacity for gear design，it is necessary to select tooth width and shaft diameter reasonably which makes minor adjustments
This volume contains the proceedings of the 13th $\mathrm{AGC^2T}$ conference, held March 14-18, 2011, in Marseille, France, together with the proceedings of the 2011 Geocrypt conference, held June ...19-24, 2011, in Bastia, France. The original research articles contained in this volume cover various topics ranging from algebraic number theory to Diophantine geometry, curves and abelian varieties over finite fields and applications to codes, boolean functions or cryptography. The international conference $\mathrm{AGC^2T}$, which is held every two years in Marseille, France, has been a major event in the area of applied arithmetic geometry for more than 25 years.
The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation ...between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.
This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that ...combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.
In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, Čech and witness complexes) built on top of totally bounded metric spaces. ...Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and Čech complexes built on top of compact spaces.
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This volume contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held from August 10-19, 2016, at Syracuse University, Syracuse, NY. ...Included are three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories. Other articles represent contributions to areas in and related to representation theory, such as noncommutative resolutions, twisted commutative algebras, and upper cluster algebras.
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