{"paper":{"title":"D'atri spaces of type k and related classes of geometries concerning jacobi operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Maria J. Druetta, Teresa Arias-Marco","submitted_at":"2011-09-29T18:05:20Z","abstract_excerpt":"In this article we continue the study of the geometry of $k$-D'Atri spaces, $% 1\\leq k$ $\\leq n-1$ ($n$ denotes the dimension of the manifold)$,$ began by the second author. It is known that $k$-D'Atri spaces, $k\\geq 1,$ are related to properties of Jacobi operators $R_{v}$ along geodesics, since she has shown that ${\\operatorname{tr}}R_{v}$, ${\\operatorname{tr}}R_{v}^{2}$ are invariant under the geodesic flow for any unit tangent vector $v$. Here, assuming that the Riemannian manifold is a D'Atri space, we prove in our main result that ${\\operatorname{tr}}R_{v}^{3}$ is also invariant under th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6607","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}