{"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":null,"pages":null},"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}
引用次数: 0
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.
Mathematics Subject Classification (2010): 53A04, 53A45, 53A55.
Received 03 May 2023; Accepted 17 January 2024
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
