{"title":"平面曲线的波利亚 f 曲率","authors":"M. Crășmăreanu, G. Pripoae","doi":"10.24193/subbmath.2024.1.14","DOIUrl":null,"url":null,"abstract":"We introduce and study a new curvature function for plane curves inspired by the weighted mean curvature of M. Gromov. We call it Pólya, being the difference between the usual curvature and the inner product of the normal vector field with the Pólya vector field of a given planar function f. We computed it for several examples, since the general problem of vanishing or constant values of this new curvature involves the general expression of f.\nMathematics Subject Classification (2010): 53A04, 53A45, 53A55.\nReceived 03 May 2023; Accepted 17 January 2024","PeriodicalId":517948,"journal":{"name":"Studia Universitatis Babes-Bolyai Matematica","volume":" 55","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Polya f-curvature of plane curves\",\"authors\":\"M. Crășmăreanu, G. Pripoae\",\"doi\":\"10.24193/subbmath.2024.1.14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce and study a new curvature function for plane curves inspired by the weighted mean curvature of M. Gromov. We call it Pólya, being the difference between the usual curvature and the inner product of the normal vector field with the Pólya vector field of a given planar function f. We computed it for several examples, since the general problem of vanishing or constant values of this new curvature involves the general expression of f.\\nMathematics Subject Classification (2010): 53A04, 53A45, 53A55.\\nReceived 03 May 2023; Accepted 17 January 2024\",\"PeriodicalId\":517948,\"journal\":{\"name\":\"Studia Universitatis Babes-Bolyai Matematica\",\"volume\":\" 55\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Universitatis Babes-Bolyai Matematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/subbmath.2024.1.14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Universitatis Babes-Bolyai Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/subbmath.2024.1.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce and study a new curvature function for plane curves inspired by the weighted mean curvature of M. Gromov. We call it Pólya, being the difference between the usual curvature and the inner product of the normal vector field with the Pólya vector field of a given planar function f. We computed it for several examples, since the general problem of vanishing or constant values of this new curvature involves the general expression of f.
Mathematics Subject Classification (2010): 53A04, 53A45, 53A55.
Received 03 May 2023; Accepted 17 January 2024
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