Riemannian Geometry and Geometric Analysis
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Beschreibung
Riemannian geometry and geometric analysis are flourishing fields with applications in physics, statistics, and machine learning. This textbook develops both fundamental concepts and more advanced topics shaped by recent progress. The 8th edition expands coverage with a systematic treatment of total scalar curvature, from which the Einstein equations, Ricci flow, and the Yamabe problem emerge, and includes new perspectives on generalized sectional and Ricci curvatures as well as Kirillov’s coadjoint orbits. It introduces core notions such as geodesics, connections, and curvature, alongside key tools of geometric analysis, including harmonic functions, forms, eigenvalues, the Dirac operator, and heat flow, and highlights major variational principles like harmonic maps, Yang–Mills, Ginzburg–Landau and Seiberg-Witten. The book offers a coherent geometric framework while equipping readers with practical methods for further study and research.
Riemannian geometry and geometric analysis are flourishing fields with applications in physics, statistics, and machine learning. This textbook develops both fundamental concepts and more advanced topics shaped by recent progress. The 8th edition expands coverage with a systematic treatment of total scalar curvature, from which the Einstein equations, Ricci flow, and the Yamabe problem emerge, and includes new perspectives on generalized sectional and Ricci curvatures as well as Kirillov’s coadjoint orbits. It introduces core notions such as geodesics, connections, and curvature, alongside key tools of geometric analysis, including harmonic functions, forms, eigenvalues, the Dirac operator, and heat flow, and highlights major variational principles like harmonic maps, Yang–Mills, Ginzburg–Landau and Seiberg-Witten. The book offers a coherent geometric framework while equipping readers with practical methods for further study and research.
Provides a solid foundation for research Starts from the very basics and leads to advanced topics Features new material on scalar, sectional and Ricci curvatures
Autor*in
Jürgen Jost
Themen in »Riemannian Geometry and Geometric Analysis«
Riemannian manifolds Lie groups symplectic geometry vector bundles Laplace operator harmonic functions curvature Dirac operator geodesics Jacobi fields symmetric spaces Kähler manifolds orbit method Ricci flow Yamabe problem