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Commentarii Mathematici Helvetici

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Volume 81, Issue 3, 2006, pp. 523–541
DOI: 10.4171/CMH/62

Published online: 2006-09-30

Pointwise taut Riemannian manifolds

Michael Leitschkis[1]

(1) Universität Köln, Germany

In the present work, we investigate pointwise taut Riemannian manifolds by using methods from Riemannian geometry, Morse theory and topology. Using ideas of Terng and Thorbergsson, we extend a result of Warner and show that a compact simply connected pointwise taut $n$-dimensional manifold is homeomorphic to a compact rank one symmetric space, if the first conjugate locus of a point is of constant multiplicity. We apply this result to study compact simply connected pointwise taut manifolds in dimensions three and four.

Keywords: Pointwise taut, Blaschke, cut locus

Leitschkis Michael: Pointwise taut Riemannian manifolds. Comment. Math. Helv. 81 (2006), 523-541. doi: 10.4171/CMH/62