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Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

The group of diffeomorphisms Diff(V) of a smooth manifold V naturally acts on the space of Riemannian metrics g on V; various classes of metrics one studies in geometry are usually invariant under Diff(V). In fact, we tend not to distinguish isometric manifolds, and a diffeomorphism f : VV establishes an isometry between (V, g) and (V, f*(g)) for each metric g. Furthermore, the geometric dictum “from local to global” suggests the study of locally defined classes of metrics on V which are moreover Diff-invariant.

Keywords

Riemannian Manifold Sectional Curvature Conjugate Point Closed Geodesic Geodesic Segment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2007

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