具有相关射影向量场的里奇几乎孤子

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2022-01-01 DOI:10.1515/advgeom-2021-0034

Ramesh Sharma, Sharief Deshmukh

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引用次数: 5

摘要

摘要证明了关联向量场是投影的Ricci几乎孤立子具有消失的Cotton张量、无散度的Bach张量和Ricci张量作为保角Killing。对于紧致情形，得到了一个关于标量曲率的尖锐不等式。我们证明了每一个完全梯度Ricci孤立子都等距于欧几里得空间和爱因斯坦空间的黎曼乘积。一个完整的K接触Ricci几乎孤立子，其关联向量场是射影的，是紧致的Einstein和Sasakian。

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Ricci almost solitons with associated projective vector field

Abstract A Ricci almost soliton whose associated vector field is projective is shown to have vanishing Cotton tensor, divergence-free Bach tensor and Ricci tensor as conformal Killing. For the compact case, a sharp inequality is obtained in terms of scalar curvature.We show that every complete gradient Ricci soliton is isometric to the Riemannian product of a Euclidean space and an Einstein space. A complete K-contact Ricci almost soliton whose associated vector field is projective is compact Einstein and Sasakian.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.