Compactness criteria for riemannian manifolds

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Ambrose, Calabi and others have obtained Ricci curvature conditions (weaker than Myers’ condition) which ensure the compactness of a complete Riemannian manifold. Using standard index form techniques we relate the problem of finding such Ricci curvature criteria to that of establishing the conjugacy of the scalar Jacobi equation. Using this relationship we obtain a Ricci curvature condition for compactness which is weaker than that of Ambrose and, in fact, which is best among a certain class of conditions.

Original languageEnglish (US)
Pages (from-to)106-110
Number of pages5
JournalProceedings of the American Mathematical Society
Volume84
Issue number1
DOIs
StatePublished - 1982

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Compactness
Riemannian Manifold
Ricci Curvature
Jacobi Equation
Conjugacy
Scalar

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Compactness criteria for riemannian manifolds. / Galloway, Gregory J.

In: Proceedings of the American Mathematical Society, Vol. 84, No. 1, 1982, p. 106-110.

Research output: Contribution to journalArticle

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