Differential and Riemannian Geometry

Detlef Laugwitz

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9781483231679
• eBook ISBN:
  9781483263984
• Topic: Mathematics
• Subtopic: Geometry
• Index: Mathematics

Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces. The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry. The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations. The book is a valuable reference for researchers interested in differential and Riemannian geometry.

Table of contents

• Front Cover
• Differential and Riemannian Geometry
• Copyright Page
• Table of Contents
• Preface to the German Edition
• Translator's Preface
• Author's Note
• CHAPTER I. Local Differential Geometry of Space Curves
• CHAPTER II. Local Differential Geometry of Surfaces
• CHAPTER III. Tensor Calculus and Riemannian Geometry
• CHAPTER IV. Further Development and Applications of Riemannian Geometry
• CHAPTER V. Selections from Differential Geometry in the Large
• APPENDIX I: From the History of Differential Geometry
• APPENDIX II: Some Prerequisite Theorems of Analysis
• APPENDIX III: Summary of Formulas
• Index