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 -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.
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Michael Leitschkis, Pointwise taut Riemannian manifolds. Comment. Math. Helv. 81 (2006), no. 3, pp. 523–541DOI 10.4171/CMH/62