Introduction to differential and Riemannian geometry

DOI10.1016/B978-0-12-814725-2.00008-XzbMath1456.53002OpenAlexW2971935723MaRDI QIDQ5133025

Xavier Pennec, Tom Fletcher, Stefan Sommer

Publication date: 12 November 2020

Published in: Riemannian Geometric Statistics in Medical Image Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/b978-0-12-814725-2.00008-x

zbMATH Keywords

homogeneous spacesRiemannian geometrygeodesicsLie algebraLie groupRiemannian manifoldsgeometric analysisgeodesically completeLie group actionembedded manifoldaction of a Lie groupKendall shape spaceatlas of a setchart of a \(d\)-dimensional manifoldconnections, curvature and topology

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20) Harmonic maps, etc. (58E20) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis (58-01) Other complex differential geometry (53C56) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry (53-01) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Connections (general theory) (53C05) Local Riemannian geometry (53B20) Methods of local Riemannian geometry (53B21)

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