Aspects Differential Geometry by Gilkey Peter (39 results)
Language: English
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Aspects of Differential Geometry V (Synthesis Lectures on Mathematics & Statistics)
Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón
Language: English
Published by Springer, 2021
Series: Book 36 of 72 - Synthesis Lectures on Mathematics & Statistics
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Language: English
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Language: English
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Language: English
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Aspects of Differential Geometry V 1ED
Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón
Language: English
Published by Springer, 2021
Series: Book 36 of 72 - Synthesis Lectures on Mathematics & Statistics
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Aspects of Differential Geometry IV (Synthesis Lectures on Mathematics and Statistics)
Esteban Calvi?o-Louzao (Author), Eduardo Garc?a-R?o (Author), Peter Gilkey (Author), JeongHyeong Park (Author), & 1 more
Language: English
Published by Morgan & Claypool, 2019
Series: Book 23 of 72 - Synthesis Lectures on Mathematics & Statistics
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Hardback. Condition: New. new copies no faults. Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested i…n affine differential geometry. We are primarily concerned with the study of affine surfaces {which} are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2.
Aspects of Differential Geometry III (Synthesis Lectures on Mathematics & Statistics)
Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón
Language: English
Published by Springer, 2017
Series: Book 17 of 72 - Synthesis Lectures on Mathematics & Statistics
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Aspects of Differential Geometry V (Synthesis Lectures on Mathematics & Statistics)
Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón
Language: English
Published by Springer, 2021
Series: Book 36 of 72 - Synthesis Lectures on Mathematics & Statistics
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Aspects of Differential Geometry IV (Synthesis Lectures on Mathematics & Statistics)
Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón
Language: English
Published by Springer, 2019
Series: Book 23 of 72 - Synthesis Lectures on Mathematics & Statistics
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Language: English
Published by Springer International Publishing, 2015
Series: Book 14 of 72 - Synthesis Lectures on Mathematics & Statistics
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 prov…ides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new. Table of Contents: Preface / Acknowledgments / Basic Notions and Concepts / Manifolds / Riemannian and Pseudo-Riemannian Geometry / Bibliography / Authors' Biographies / Index.
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paperback. Condition: New. Paperback. Pub Date: 2021-03-01 Pages: 188 Language: English Publisher: Harbin Institute of Technology Press All Aspects of Differential Geometry. Volume One (English) is an imported version of the original English mathematics textbook. One of a series of books.?The title of the Chinese book can be tra…nslated as All Aspects of Differential Geometry (Volume One).?All Aspects of Differential Geometry. Volume One (English) consists of three chapters.?Chapter 1 introduces multivariable calculus...
Language: English
Published by Springer, 2015
Series: Book 15 of 72 - Synthesis Lectures on Mathematics & Statistics
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book…I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology ofcompact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.
Language: English
Published by Morgan & Claypool Publishers, 2019
Series: Book 23 of 72 - Synthesis Lectures on Mathematics & Statistics
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Soft cover. Condition: New. 8vo (23.5 cm), XVII, 149 pp. Laminated wrappers. Synopsis: Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be ac…cessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces which are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group ℝ² is Abelian and the ???? + ?? group is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type ?? surfaces. These are the left-invariant affine geometries on ℝ². Associating to each Type ?? surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue ?? = -1 turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type ?? surfaces; these are the left-invariant affine geometries on the ???? + ?? group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere ??². The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension.
Language: English
Published by Springer, 2015
Series: Book 14 of 72 - Synthesis Lectures on Mathematics & Statistics
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Taschenbuch. Condition: Neu. Aspects of Differential Geometry I | Peter Gilkey (u. a.) | Taschenbuch | Synthesis Lectures on Mathematics & Statistics | xiii | Englisch | 2015 | Springer | EAN 9783031012792 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]spri…nger[dot]com | Anbieter: preigu.
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Published by Springer, 2015
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Taschenbuch. Condition: Neu. Aspects of Differential Geometry II | Peter Gilkey (u. a.) | Taschenbuch | Synthesis Lectures on Mathematics & Statistics | xiii | Englisch | 2015 | Springer | EAN 9783031012808 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]spr…inger[dot]com | Anbieter: preigu.
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Published by MORGAN & CLAYPOOL, 2017
Series: Book 17 of 72 - Synthesis Lectures on Mathematics & Statistics
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries…. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new. Table of Contents: Preface / Acknowledgments / Basic Notions and Concepts / Manifolds / Riemannian and Pseudo-Riemannian Geometry / Bibliography / Authors' Biographies / Index 156 pp. Englisch.
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced mat…erial than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs. 160 pp. Englisch.
Aspects of Differential Geometry III (Synthesis Lectures on Mathematics & Statistics)
Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón
Language: English
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Aspects of Differential Geometry III (Synthesis Lectures on Mathematics & Statistics)
Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón
Language: English
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Published by Springer, Berlin|Springer International Publishing|Morgan & Claypool|Springer, 2015
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject we have not attempted an encyclopedic treatment. Book II deals with mor…e advanced material than Book I and is .
Language: English
Published by Springer, Berlin|Springer International Publishing|Morgan & Claypool|Springer, 2015
Series: Book 14 of 72 - Synthesis Lectures on Mathematics & Statistics
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject we have not attempted an encyclopedic treatment. In Book I, we focus on… preliminaries. Chapter 1 provides an i.
