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Fundamentals of Differential Geometry

Posted By: AvaxGenius

Date: 15 Nov 2023 07:15:58

Fundamentals of Differential Geometry by Serge Lang
English | PDF | 1999 | 553 Pages | ISBN : 038798593X | 63.9 MB

The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry. The size of the book influenced where to stop, and there would be enough material for a second volume (this is not a threat). At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differen tiable maps in them (immersions, embeddings, isomorphisms, etc. ).

Science Riemannian geometry Differential Geometry Geometry

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Nonstandard Analysis in Practice

Posted By: AvaxGenius

Date: 2 Nov 2023 15:44:07

Nonstandard Analysis in Practice by Francine Diener, Marc Diener
English | PDF | 1995 | 262 Pages | ISBN : 3540602976 | 34.3 MB

The purpose of this book is to provide an effective introduction to nonstandard methods. A short tutorial giving the necessary background, is followed by applications to various domains, independent from each other. These include complex dynamical systems, stochastic differential equations, smooth and algebraic curves, measure theory, the external calculus, with some applications to probability. The authors have been using Nonstandard Analysis for many years in their research. They all belong to the growing nonstandard school founded by G. Reeb, which is attracting international and interdisciplinary interest.

Science Martingale differential geometry Riemannian geometry Real Functions Mathematical Logic Stochastic Processes

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Variational Problems in Riemannian Geometry: Bubbles, Scans and Geometric Flows

Posted By: AvaxGenius

Date: 29 Jul 2023 18:47:19

Variational Problems in Riemannian Geometry: Bubbles, Scans and Geometric Flows by Paul Baird, Ali Fardoun, Rachid Regbaoui, Ahmad Soufi
English | PDF | 2004 | 158 Pages | ISBN : 3764324325 | 21.3 MB

This volume has grown from a conference entitled Harmonic Maps, Minimal Sur faces and Geometric Flows which was held at the Universite de Bretagne Occi dentale from July 7th-12th, 2002, in the town of Brest in Brittany, France. We welcomed many distinguished mathematicians from around the world and a dy namic meeting took place, with many fruitful exchanges of ideas.

Science Differential geometry Finsler geometry Riemannian geometry Differential Geometry Functional Analysis Differential Equations Geometry

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Osserman Manifolds in Semi-Riemannian Geometry

Posted By: AvaxGenius

Date: 24 Mar 2023 04:32:36

Osserman Manifolds in Semi-Riemannian Geometry by Eduardo García-Río , Demir N. Kupeli , Ramón Vázquez-Lorenzo
English | PDF | 2002| 178 Pages | ISBN : 3540431446 | 14.6 MB

The subject of this book is Osserman semi-Riemannian manifolds, and in particular, the Osserman conjecture in semi-Riemannian geometry. The treatment is pitched at the intermediate graduate level and requires some intermediate knowledge of differential geometry. The notation is mostly coordinate-free and the terminology is that of modern differential geometry. Known results toward the complete proof of Riemannian Osserman conjecture are given and the Osserman conjecture in Lorentzian geometry is proved completely. Counterexamples to the Osserman conjuncture in generic semi-Riemannian signature are provided and properties of semi-Riemannian Osserman manifolds are investigated.

Science Osserman Conjecture Riemannian geometry differential geometry Differential Geometry Computational Physics Physics Geometry

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Holomorphic Curves in Symplectic Geometry

Posted By: AvaxGenius

Date: 24 Mar 2023 03:49:32

Holomorphic Curves in Symplectic Geometry by Michèle Audin, Jacques Lafontaine
English | PDF | 1994 | 333 Pages | ISBN : 3764329971 | 44.2 MB

This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises.

Science Immersion Riemannian geometry Differential Geometry Geometry

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Differential Geometry of Spray and Finsler Spaces (Repost)

Posted By: AvaxGenius

Date: 23 Mar 2023 17:59:06

Differential Geometry of Spray and Finsler Spaces (Repost)

Differential Geometry of Spray and Finsler Spaces by Zhongmin Shen
English | PDF | 2001 | 260 Pages | ISBN : 0792368681 | 16.2MB

In this book we study sprays and Finsler metrics. Roughly speaking, a spray on a manifold consists of compatible systems of second-order ordinary differential equations. A Finsler metric on a manifold is a family of norms in tangent spaces, which vary smoothly with the base point. Every Finsler metric determines a spray by its systems of geodesic equations. Thus, Finsler spaces can be viewed as special spray spaces. On the other hand, every Finsler metric defines a distance function by the length of minimial curves. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces. In 1854, B. Riemann introduced the Riemann curvature for Riemannian spaces in his ground-breaking Habilitationsvortrag.

Science Finsler geometry Riemannian geometry Geometry Differential Geometry Finsler Spaces

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Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions (Repost)

Posted By: AvaxGenius

Date: 23 Mar 2023 12:18:37

Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions (Repost)

Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions by Michel L. Lapidus , Machiel Frankenhuysen
English | PDF | 2000 | 277 Pages | ISBN : 0817640983 | 21.76 MB

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string.

Riemannian geometry Science differential geometry Algebraic geometry partial differential equations geometry Number Theory Algebraic Geometry Differential Geometry Fractal Geometry Geometry Zeta Functions Fractal Strings Complex Dimensions Dimensions

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A Differential Approach to Geometry: Geometric Trilogy III

Posted By: AvaxGenius

Date: 9 Nov 2021 05:32:40

This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties.

surfaces Mathematics differential geometry geometry Riemannian geometry Statistics Geometric Trilogy Geometry

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A Differential Approach to Geometry: Geometric Trilogy III

Posted By: AvaxGenius

Date: 3 Jan 2021 21:17:53

surfaces 53A45 53C22 Mathematics and Statistics Riemannian geometry 53A04 53A05 curves Euler-Poincaré characteristics 53C45 ePub 53B20 Science differential geometry Mathematics 53A55

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Geometry and Physics

Posted By: AvaxGenius

Date: 28 Jun 2020 02:30:53

"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics.

Sigma model Riemannian geometry Quantum Field Theory Science Mathematics Physics

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