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Books
Differential Geometry
Surveys in Differential Geometry, Vol. 21 (2016): Advances in geometry and mathematical physics
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Author: [various contributors]

This volume consists of articles by speakers at the Conference on Geometry and Topology held at Harvard University in 2014. Included are: Camillo De Lellis, on the size of the singular set of areaminimizing currents; Simon Donaldson, on KählerEinstein metrics and algebraic structures on limit spaces; Mark Gross, on theta functions and mirror symmetry; Nigel Hitchin, on Higgs bundles and diffeomorphism groups; Fernando Marques, on topology of the space of cycles and existence of minimal varieties; William Meeks, on constant mean curvature surfaces; Richard Thomas, on the proof of the KKV conjecture; Claire Voisin, on stable birational invariants and the Luroth problem; and MuTao Wang, on energy, momentum, and center of mass in general relativity.


Geometric Formulas (Quick Study: Academic)
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Author: Inc. BarCharts
Brand: QuickStudy

6page laminated guide includes: ·general terms ·lines ·line segments ·rays ·angles ·transversal line angles ·polygons ·circles ·theorems & relationships ·postulates ·geometric formulas
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Geometry Part 2 (Quickstudy Reference Guides  Academic)
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Author: Inc. BarCharts
Brand: QuickStudy

Part 2 of our coverage of the fundamental structure of geometry.
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Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
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Author: Manfredo P. do Carmo

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, wellwritten exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.
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Torus Actions on Symplectic Manifolds (Progress in Mathematics)
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Author: Michèle Audin
Brand: Michele Audin

The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity results, it contains much more material, in particular lots of new examples and exercises.
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 Torus Actions on Symplectic Manifolds


Spectral Geometry, Riemannian Submersions, and the GromovLawson Conjecture (Studies in Advanced Mathematics)
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Author: Peter B. Gilkey
Brand: Brand: CRC Press

This cuttingedge, standardsetting text explores the spectral geometry of Riemannian submersions. Working for the most part with the form valued Laplacian in the class of smooth compact manifolds without boundary, the authors study the relationshipif anybetween the spectrum of Dp on Y and Dp on Z, given that Dp is the p form valued Laplacian and pi: Z ® Y is a Riemannian submersion.
After providing the necessary background, including basic differential geometry and a discussion of Laplace type operators, the authors address rigidity theorems. They establish conditions that ensure that the pull back of every eigenform on Y is an eigenform on Z so the eigenvalues do not change, then show that if a single eigensection is preserved, the eigenvalues do not change for the scalar or Bochner Laplacians. For the form valued Laplacian, they show that if an eigenform is preserved, then the corresponding eigenvalue can only increase. They generalize these results to the complex setting as well. However, the spinor setting is quite different. For a manifold with nontrivial boundary and imposed Neumann boundary conditions, the result is surprisingthe eigenvalues can change. Although this is a relatively rare phenomenon, the authors give examplesa circle bundle or, more generally, a principal bundle with structure group G where the first cohomology group H1(G;R) is non trivial. They show similar results in the complex setting, show that eigenvalues can decrease in the spinor setting, and offer a list of unsolved problems in this area. Moving to some related topics involving questions of positive curvature, for the first time in mathematical literature the authors establish a link between the spectral geometry of Riemannian submersions and the GromovLawson conjecture. Spectral Geometry, Riemannian Submersions, and the GromovLawson Conjecture addresses a hot research area and promises to set a standard for the field. Researchers and applied mathematicians interested in mathematical physics and relativity will find this work both fascinating and important.
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An Introduction to Manifolds (Universitext)
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Author: Loring W. Tu

Manifolds, the higherdimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite pointset topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a onesemester graduate or advanced undergraduate course, as well as by students engaged in selfstudy. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
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The Wheel Of Time: The Shamans Of Mexico Their Thoughts About Life Death And The Universe
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Author: Carlos Castaneda
Brand: Unknown

Worldrenowned bestselling author Carlos Castaneda's Selection of his wrtings on the shamans of ancient Mexico.
Originally drawn to Yaqui Indian spiritual leader don Juan Matus for his knowledge of mindaltering plants, bestselling author Carlos Castaneda soon immersed himself in the sorcerer’s magical world entirely. Ten years after his first encounter with the shaman, Castaneda examines his field notes and comes to understand what don Juan knew all along—that these plants are merely a means to understanding the alternative realities that one cannot fully embrace on one’s own. In Journey to Ixtlan, Carlos Castaneda introduces readers to this new approach for the first time and explores, as he comes to experience it himself, his own final voyage into the teachings of don Juan, sharing with us what it is like to truly “stop the world” and perceive reality on his own terms.
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 The Wheel of Time: The Shamans of Ancient Mexico, Their Thoughts About Life, Death and the Universe
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Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)
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Author: John Lee
Brand: Brand: Springer

This book is an introductory graduatelevel textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of firstorder partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
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Lectures On The Geometry Of Manifolds
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Author: Liviu I Nicolaescu
Brand: Nicolaescu Liviu I

The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and pointset topology. The book's guiding philosophy is, in the words of Newton, that “in learning the sciences examples are of more use than precepts”. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue. While we present most of the local aspects of classical differential geometry, the book has a “global and analytical bias”. We develop many algebraictopological techniques in the special context of smooth manifolds such as Poincaré duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss–Bonnet theorem. We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand Hölder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an indepth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators. The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.
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 Lectures on the Geometry of Manifolds
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