Much work has been done on spaces with large groups of motions, but very little on conditions under which the number of motions is finite. The best known classical result in this direction states that a compact Riemann space with negative curvature has a finite group of motions. Section 18 discusses questions of this type and in particular extends the mentioned theorem in several ways.
KeywordsFundamental Group Conjugate Point Closed Geodesic Universal Covering Space Domain Invariance
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