Titlebook: Riemannian Geometry and Geometric Analysis; Jürgen Jost Textbook 2017Latest edition Springer International Publishing AG 2017 53B21, 53L20

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Chapter 2 Lie Groups and Vector Bundles,ll therefore use this opportunity to also discuss Lie groups and their infinitesimal versions, the Lie algebras. Complex and symplectic structures are also discussed. Spin geometry is treated in detail.

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Chapter 4 Connections and Curvature,tional. The fundamental connection of Riemannian geometry is the Levi-Civita connection, which, in particular, respects the metric. From that connection, we obtain the Riemann curvature tensor. This in turn defines the basic curvature notions of Riemannian geometry, sectional and Ricci curvature. Th

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Chapter 3 The Laplace Operator and Harmonic Differential Forms,rential forms and de Rham cohomology groups, together with the essential tools from elliptic PDE for treating these groups. The existence of harmonic forms representing cohomology classes is proved both by a variational method and by the heat flow method. The spectrum of the Laplacian on differential forms is also discussed.

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0172-5939 ectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature..From the reviews:.“This book provides a very readable introduction to Riemannian geomet978-3-319-61859-3978-3-319-61860-9Series ISSN 0172-5939 Series E-ISSN 2191-6675