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OverviewNowadays, curvature conditions are one of the powerful tools to study the geometry of Riemannian manifolds. In particular cases, one can obtain geometric properties of a manifold from the curvature operator and its derivatives or vice versa. Now, through this notes we will work in both directions. First, we obtain geometric properties of manifolds working with Ledger's conditions. In particular, we solve the problem of checking if the three-parameter families of six and twelve-dimensional flag manifolds constructed by N. R. Wallach are D'Atri spaces and we obtain the classification of 4-dimensional homogeneous D'Atri spaces. Finally, we introduce the concept of Jacobi osculating rank of a Riemannian g. o. space and, we show how this new concept provide properties of the curvature operator (or, more accurately, of the Jacobi operator) and its derivatives using the geometric properties of a given g. o. space. We also show the known applications and work on explicit examples. Full Product DetailsAuthor: Teresa Arias-MarcoPublisher: LAP Lambert Academic Publishing Imprint: LAP Lambert Academic Publishing Dimensions: Width: 15.20cm , Height: 0.70cm , Length: 22.90cm Weight: 0.191kg ISBN: 9783838321745ISBN 10: 383832174 Pages: 124 Publication Date: 09 June 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |