{"query": "S. Bochner 1946 — Vector fields and Ricci curvature", "count": 5, "results": [{"id": "card_src_mill_bochner_1946", "title": "S. Bochner 1946 — Vector fields and Ricci curvature", "shelf": "millennium", "surface": "secular", "snippet": "S. Bochner (1946). Vector fields and Ricci curvature. Bull. Amer. Math. Soc. 52 (1946) 776–797. DOI 10.1090/S0002-9904-1946-08647-4. Canonical: https://doi.org/10.1090/S0002-9904-1946-08647-4. Free co", "authority_tier": "reference", "source": "S. Bochner (1946), Bull. Amer. Math. Soc. 52 (1946) 776–797", "readable": false, "generated": false}, {"id": "card_joint_bochner_vanishing", "title": "Positive Ricci curvature kills harmonic one-forms", "shelf": "codex", "surface": "secular", "snippet": "Bochner (1946): a closed manifold with positive Ricci curvature carries no non-zero harmonic one-form, so its first Betti number is zero - a Hodge-theoretic conclusion from the very hypothesis Hamilto", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_myers_1941", "title": "S. B. Myers 1941 — Riemannian manifolds with positive mean curvature", "shelf": "millennium", "surface": "secular", "snippet": "S. B. Myers (1941). Riemannian manifolds with positive mean curvature. Duke Math. J. 8 (1941) 401–404. DOI 10.1215/S0012-7094-41-00832-3. Canonical: https://doi.org/10.1215/S0012-7094-41-00832-3. No f", "authority_tier": "reference", "source": "S. B. Myers (1941), Duke Math. J. 8 (1941) 401–404", "readable": false, "generated": false}, {"id": "card_src_pron_bochner", "title": "bochner", "shelf": "pronunciation", "surface": "secular", "snippet": "bochner: pronounced (ARPABET) B AA1 K N ER0. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_src_pron_harv", "title": "harv", "shelf": "pronunciation", "surface": "secular", "snippet": "harv: pronounced (ARPABET) HH AA1 R V. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_src_mill_bochner_1946"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}