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    https://sophisticatedspectra.com/article/drosia-serenity-a-modern-oasis-in-the-heart-of-larnaca.2521391.html

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    Applied Differential Geometry

    Posted By: roxul
    Applied Differential Geometry

    Burke, "Applied Differential Geometry"
    English | ISBN: 0521269296 | 2008 | 436 pages | PDF | 163 MB

    Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint

    Posted By: AvaxGenius
    Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint

    Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint by Gregor Fels , Alan Huckleberry , Joseph A. Wolf
    English | PDF (True) | 2006 | 342 Pages | ISBN : 0817643915 | 2.8 MB

    This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?ag domains. Some of the methods are now standard, but many are new. The exposition is carried out from the viewpoint of complex algebraic and differential geometry. Except for certain foundational material,whichisreadilyavailablefromstandardtexts,itisessentiallyself-contained; at points where this is not the case we give extensive references. After developing the background material on complex ?ag manifolds and rep- sentationtheory, wegiveanexposition(withanumberofnewresults)ofthecomplex geometric methods that lead to our characterizations of (group theoretically de?ned) cycle spaces and to a number of consequences.

    Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

    Posted By: AvaxGenius
    Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

    Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics by Claudio Bartocci , Ugo Bruzzo , Daniel Hernández Ruipérez
    English | PDF (True) | 2009 | 435 Pages | ISBN : 0817632468 | 3.9 MB

    Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character.

    Differential Geometry of Varieties with Degenerate Gauss Maps (Repost)

    Posted By: AvaxGenius
    Differential Geometry of Varieties with Degenerate Gauss Maps (Repost)

    Differential Geometry of Varieties with Degenerate Gauss Maps by Maks A. Akivis , Vladislav V. Goldberg
    English | PDF | 2004 | 272 Pages | ISBN : 0387404635 | 23.5 MB

    In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means of these methods, the authors discover the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

    Riemannian Geometry

    Posted By: AvaxGenius
    Riemannian Geometry

    Riemannian Geometry by Sylvestre Gallot , Dominique Hulin , Jacques Lafontaine
    English | PDF (True) | 2004 | 332 Pages | ISBN : 3540204938 | 3.2 MB

    From the preface:Many years have passed since the first edition. However, the encouragements of various readers and friends have persuaded us to write this third edition. During these years, Riemannian Geometry has undergone many dramatic developments. Here is not the place to relate them. The reader can consult for instance the recent book [Br5]. of our “mentor” Marcel Berger. However, Riemannian Geometry is not only a fascinating field in itself. It has proved to be a precious tool in other parts of mathematics. In this respect, we can quote the major breakthroughs in four-dimensional topology which occurred in the eighties and the nineties of the last century (see for instance [L2]). These have been followed, quite recently, by a possibly successful approach to the Poincaré conjecture. In another direction, Geometric Group Theory, a very active field nowadays (cf. [Gr6]), borrows many ideas from Riemannian or metric geometry. But let us stop hogging the limelight. This is justa textbook. We hope that our point of view of working intrinsically with manifolds as early as possible, and testing every new notion on a series of recurrent examples (see the introduction to the first edition for a detailed description), can be useful both to beginners and to mathematicians from other fields, wanting to acquire some feeling for the subject.

    The Implicit Function Theorem: History, Theory, and Applications

    Posted By: AvaxGenius
    The Implicit Function Theorem: History, Theory, and Applications

    The Implicit Function Theorem: History, Theory, and Applications by Steven G. Krantz , Harold R. Parks
    English | PDF (True) | 2003 | 168 Pages | ISBN : 1461265932 | 18.1 MB

    The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non- smooth functions, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash–Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve. "The Implicit Function Theorem" is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas.

    Differential Geometry: Structures on Manifolds and Submanifolds

    Posted By: readerXXI
    Differential Geometry: Structures on Manifolds and Submanifolds

    Differential Geometry: Structures on Manifolds and Submanifolds
    by Mohammad Hasan Shahid
    English | 2024 | ISBN: 3725821895 | 270 Pages | PDF | 3.87 MB

    A Geometric Approach to Differential Forms

    Posted By: AvaxGenius
    A Geometric Approach to Differential Forms

    A Geometric Approach to Differential Forms by David Bachman
    English | PDF (True) | 2006 | 141 Pages | ISBN : 0817644997 | 1.2 MB

    The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually.

    Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers

    Posted By: AvaxGenius
    Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers

    Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers by P. M. Gadea , J. Muñoz Masqué
    English | PDF (True) | 2001 | 446 Pages | ISBN : 904813563X | 4 MB

    A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Hence, there arises the natural question—how to attain a deeper understanding? One well-known way to gain an understanding is through underpinning the d- nitions, theorems and constructions with hierarchies of examples, counterexamples and exercises. Their choice, construction and logical order is for any teacher in global analysis an interesting, important and fun creating task.

    Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear Problems

    Posted By: AvaxGenius
    Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear Problems

    Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear Problems by Michel Demazure
    English | PDF (True) | 2000 | 304 Pages | ISBN : 3540521186 | 38.1 MB

    Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.

    Flow Lines and Algebraic Invariants in Contact Form Geometry

    Posted By: AvaxGenius
    Flow Lines and Algebraic Invariants in Contact Form Geometry

    Flow Lines and Algebraic Invariants in Contact Form Geometry by Abbas Bahri
    English | PDF (True) | 2003 | 219 Pages | ISBN : 0817643184 | 26.6 MB

    This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, this work develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields.

    Symplectic Geometry of Integrable Hamiltonian Systems

    Posted By: AvaxGenius
    Symplectic Geometry of Integrable Hamiltonian Systems

    Symplectic Geometry of Integrable Hamiltonian Systems by Michèle Audin , Ana Cannas Silva , Eugene Lerman
    English | PDF (True) | 2003 | 225 Pages | ISBN : 3764321679 | 16.1 MB

    Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book).

    An Introduction to Compactness Results in Symplectic Field Theory (Repost)

    Posted By: AvaxGenius
    An Introduction to Compactness Results in Symplectic Field Theory (Repost)

    An Introduction to Compactness Results in Symplectic Field Theory by Casim Abbas
    English | PDF (True) | 2014 | 257 Pages | ISBN : 3642315429 | 2.3 MB

    This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade. The author presents a systematic introduction providing a lot of background material, much of which is scattered throughout the literature. Since the content grew out of lectures given by the author, the main aim is to provide an entry point into symplectic field theory for non-specialists and for graduate students. Extensions of certain compactness results, which are believed to be true by the specialists but have not yet been published in the literature in detail, top off the scope of this monograph.

    Morse Theory and Floer Homology

    Posted By: AvaxGenius
    Morse Theory and Floer Homology

    Morse Theory and Floer Homology by Michèle Audin , Mihai Damian
    English | PDF (True) | 2014 | 595 Pages | ISBN : 1447154959 | 4.9 MB

    This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold.

    Encyclopedia of Distances, Third Edition

    Posted By: AvaxGenius
    Encyclopedia of Distances, Third Edition

    Encyclopedia of Distances, Third Edition by Michel Marie Deza , Elena Deza
    English | PDF (True) | 2014 | 731 Pages | ISBN : 3662518686 | 6.3 MB

    This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances.