Resumen de Pointwise taut Riemannian manifolds

Michael Leitschkis

• 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