{"paper":{"title":"Geometry of $G$-Structures via the Intrinsic Torsion","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kamil Niedzialomski","submitted_at":"2015-03-12T14:27:47Z","abstract_excerpt":"We study the geometry of a $G$-structure $P$ inside the oriented orthonormal frame bundle ${\\rm SO}(M)$ over an oriented Riemannian manifold $M$. We assume that $G$ is connected and closed, so the quotient ${\\rm SO}(n)/G$, where $n=\\dim M$, is a normal homogeneous space and we equip ${\\rm SO}(M)$ with the natural Riemannian structure induced from the structure on $M$ and the Killing form of ${\\rm SO}(n)$. We show, in particular, that minimality of $P$ is equivalent to harmonicity of an induced section of the homogeneous bundle ${\\rm SO}(M)\\times_{{\\rm SO}(n)}{\\rm SO}(n)/G$, with a Riemannian m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03740","kind":"arxiv","version":3},"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"}