{"paper":{"title":"Generalized Chen's inequalities for Riemannian submersions and Riemannian maps with Applications","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ravindra Singh","submitted_at":"2026-06-17T06:05:25Z","abstract_excerpt":"In this paper, we establish generalized B.-Y. Chen inequalities for Riemannian submersions and Riemannian maps between Riemannian manifolds by employing the generalized $\\delta$-invariants introduced by Chen. We derive optimal inequalities involving the generalized $\\delta$-invariants associated with the vertical and horizontal distributions together with extrinsic invariants determined by the second fundamental tensors of the submersion and the Riemannian map. Furthermore, we characterize the equality cases through precise algebraic conditions on the corresponding shape operators, providing t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18725","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18725/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}