Curvature of space and time, with an introduction to geometric analysis

著者

• Stavrov, Iva

書誌事項

Curvature of space and time, with an introduction to geometric analysis

Iva Stavrov

（Student mathematical library, v. 93 . IAS/Park City mathematical subseries）

American Mathematical Society , Institute for Advanced Study, c2020

• : pbk

注記

Includes bibliographical references (p. 239) and index

内容説明・目次

内容説明

This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College. This book is published in cooperation with IAS/Park City Mathematics Institute.

目次

Introduction to Riemannian geometry Differential calculus with tensors Curvature General relativity Introduction to geometry analysis Bibliography Index

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BC02574519
• ISBN:
  • 9781470456283
• LCCN: 2020035487
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: [Providence, R.I.],[Princeton, N.J.]
• ページ数/冊数: xi, 243 p.
• 大きさ: 22 cm
• 分類:
  • LCC : QC173.6
  • DC23 : 530.1101/516373
  • DC23 : 530.1101516373
• 件名:
  • LCSH : General relativity (Physics) -- Mathematics
  • LCSH : Curvature
  • LCSH : Space and time
  • LCSH : Geometry, Riemannian
  • LCSH : Geometry, Differential
  • LCSH : Geometric analysis
  • FREE : Relativity and gravitational theory -- Instructional exposition (textbooks, tutorial papers, etc.) msc
  • FREE : Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Instructional exposition (textbooks, tutorial papers, etc.) msc
• 親書誌ID:
  • BA42504671