具有垂直广义Berger型变形Sasaki度量的切束研究

IF 0.7 4区数学 Q2 MATHEMATICS

Hacettepe Journal of Mathematics and Statistics Pub Date : 2023-01-01 DOI:10.15672/hujms.1091758

Saadia Chaoui̇, A. Zagane, A. Gezer, N. Djaa

{"title":"具有垂直广义Berger型变形Sasaki度量的切束研究","authors":"Saadia Chaoui̇, A. Zagane, A. Gezer, N. Djaa","doi":"10.15672/hujms.1091758","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce the vertical generalized Berger type deformed Sasaki metric on the tangent bundle $TM$ over an anti-paraK\\\"{a}hler manifold as a new natural metric. Firstly, we investigate the Levi-Civita connection of this metric and then calculate all forms of the Riemannian curvature tensors. Also, we present some results concerning curvature properties. Finally, we study the geometry of $\\varphi $-unit tangent bundle equipped with vertical generalized Berger type deformed Sasaki metric.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"9 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A study on tangent bundles with vertical generalized Berger type deformed Sasaki metric\",\"authors\":\"Saadia Chaoui̇, A. Zagane, A. Gezer, N. Djaa\",\"doi\":\"10.15672/hujms.1091758\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce the vertical generalized Berger type deformed Sasaki metric on the tangent bundle $TM$ over an anti-paraK\\\\\\\"{a}hler manifold as a new natural metric. Firstly, we investigate the Levi-Civita connection of this metric and then calculate all forms of the Riemannian curvature tensors. Also, we present some results concerning curvature properties. Finally, we study the geometry of $\\\\varphi $-unit tangent bundle equipped with vertical generalized Berger type deformed Sasaki metric.\",\"PeriodicalId\":55078,\"journal\":{\"name\":\"Hacettepe Journal of Mathematics and Statistics\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hacettepe Journal of Mathematics and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.15672/hujms.1091758\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1091758","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文引入了反parak \ {a}hler流形上切束$TM$上的垂直广义Berger型变形Sasaki度规作为一种新的自然度规。首先，我们研究了该度规的列维-奇维塔连接，然后计算了黎曼曲率张量的所有形式。同时，我们也给出了一些关于曲率性质的结果。最后，我们研究了具有垂直广义Berger型变形Sasaki度量的$\varphi $-单位切线束的几何形状。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A study on tangent bundles with vertical generalized Berger type deformed Sasaki metric

In this paper, we introduce the vertical generalized Berger type deformed Sasaki metric on the tangent bundle $TM$ over an anti-paraK\"{a}hler manifold as a new natural metric. Firstly, we investigate the Levi-Civita connection of this metric and then calculate all forms of the Riemannian curvature tensors. Also, we present some results concerning curvature properties. Finally, we study the geometry of $\varphi $-unit tangent bundle equipped with vertical generalized Berger type deformed Sasaki metric.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.