Killing Fields

Part of the Graduate Texts in Mathematics book series (GTM, volume 171)


In this chapter we begin with a section on some general results about Killing fields and their relationship to the isometry group. This is used in the 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.


Euler Characteristic Isometry Group Positive Sectional Curvature Killing Field Hopf Fibration 
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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA

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