{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:24:40Z","timestamp":1760149480638,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,12]],"date-time":"2023-08-12T00:00:00Z","timestamp":1691798400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11961061","11461064"],"award-info":[{"award-number":["11961061","11461064"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space\u2013time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we find differential equations of Finsler warped product metrics with vanishing \u03c7-curvature or vanishing H-curvature. Furthermore, we show that, for Finsler warped product metrics, the \u03c7-curvature vanishes if and only if the H-curvature vanishes.<\/jats:p>","DOI":"10.3390\/axioms12080784","type":"journal-article","created":{"date-parts":[[2023,8,14]],"date-time":"2023-08-14T11:07:10Z","timestamp":1692011230000},"page":"784","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finsler Warped Product Metrics with Special Curvature Properties"],"prefix":"10.3390","volume":"12","author":[{"given":"Lingen","family":"Sun","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"}]},{"given":"Xiaoling","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"}]},{"given":"Mengke","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"184","DOI":"10.4153\/CMB-2011-163-4","article-title":"On Some Non-Riemannian Quantities in Finsler Geometry","volume":"56","author":"Shen","year":"2013","journal-title":"Can. 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