Geodesic connectedness of affine manifolds

We discuss new sufficient conditions under which an affine manifold ( M , ∇ ) is geodesically connected. These conditions are shown to be essentially weaker than those discussed in groundbreaking work by Beem and Parker and in recent work by Alexander and Karr, with the added advantage that they yie...

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Bibliographic Details
Published inAnnali di matematica pura ed applicata Vol. 200; no. 3; pp. 1135 - 1148
Main Authors Costa e Silva, Ivan P., Flores, José L.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Springer Nature B.V
Subjects
Manifolds
Mathematics
Mathematics and Statistics
Semi-Riemannian manifolds
Geodesic connectivity
Affine manifolds
Primary 53C22
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Summary:We discuss new sufficient conditions under which an affine manifold ( M , ∇ ) is geodesically connected. These conditions are shown to be essentially weaker than those discussed in groundbreaking work by Beem and Parker and in recent work by Alexander and Karr, with the added advantage that they yield an elementary proof of the main result.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-020-01028-8