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Isometries of Elliptic 3‐Manifolds
Author(s) -
McCullough Darryl
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002782
Subject(s) - bijection , mathematics , pure mathematics , invariant (physics) , isometry (riemannian geometry) , constant (computer programming) , isometry group , mathematical analysis , combinatorics , mathematical physics , computer science , programming language
The closed 3‐manifolds of constant positive curvature were classified long ago by Seifert and Threlfall. Using well‐known information about the orthogonal group O(4), their full isometry groups Isom( M ) are calculated. It is determined which elliptic 3‐manifolds admit Seifert fiberings that are invariant under all isometries, and it is verified that the inclusion of Isom( M ) to Diff( M ) is a bijection on path components.