Titlebook: Riemannian Geometry; Peter Petersen Textbook 2016Latest edition Springer International Publishing AG 2016 Riemannian geometry textbook ado

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Curvature, the realm of geometry. The most elementary way of defining curvature is to set it up as an integrability condition. This indicates that when it vanishes it should be possible to solve certain differential equations, e.g., that the metric is Euclidean. This was in fact one of Riemann’s key insights.

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Killing Fields, subsequent section to prove Bochner’s theorems about the lack of Killing fields on manifolds with negative Ricci curvature. In the last section we present several results about how Killing fields influence the topology of manifolds with positive sectional curvature. This is a somewhat more recent line of inquiry.

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Derivatives,This chapter introduces several important notions of derivatives of tensors. In chapters 5 and 6 we also introduce partial derivatives of functions into Riemannian manifolds.

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Convergence,In this chapter we offer an introduction to several of the convergence ideas for Riemannian manifolds.

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Peter PetersenIncludes a substantial addition of unique and enriching exercises.Exists as one of the few Works to combine both the geometric parts of Riemannian geometry and analytic aspects of the theory.Presents

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