{"paper":{"title":"Some Characteristics of Almost $\\omega$-Bach Solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Arindam Bhattacharyya, Hemangi Madhusudan Shah, Paritosh Ghosh","submitted_at":"2025-05-30T07:58:47Z","abstract_excerpt":"In this article, we introduce $\\omega$-Bach tensor corresponding to one form $\\omega$ and correspondingly introduce almost $\\omega$-Bach solitons, thereby generalizing the existing notion of Bach tensor and almost Bach solitons. We characterize almost $\\omega$-Bach solitons, when the potential vector field of the soliton generates an infinitesimal harmonic transformation or is an affine conformal vector field, or is a projective vector field or is a Killing vector field, when the $\\omega$-Bach tensor is divergence free, or is a harmonic $1$ form or is a Killing $1$-form. We generalize some of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24316","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/2505.24316/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"}