A note on the triviality of gradient solitons of the Ricci-Bourguignon flow

被引：4

作者：

Cunha, Antonio W. ^{[1
]}

Silva, Antonio N., Jr. ^{[1
]}

De Lima, Eudes L. ^{[2
]}

De Lima, Henrique F. ^{[3
]}

机构：

[1] Univ Fed Piaui, Dept Posgrad Matemat, BR-64049550 Teresina, Piaui, Brazil

[2] Univ Fed Campina Grande, Unidade Acad Ciencias Exatas & Nat, BR-58900000 Cajazeiras, Paraiba, Brazil

[3] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil

来源：

ARCHIV DER MATHEMATIK | 2023年 / 120卷 / 01期

关键词：

Ricci-Bourguignon flow; Gradient p-Einstein solitons; Constant scalar curvature; Convergence at infinity; Polynomial volume growth; Stochastic completeness; MAXIMUM PRINCIPLE; MANIFOLDS;

D O I：

10.1007/s00013-022-01803-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Under appropriate constraints on the sign of the Ricci curvature, we investigate the triviality of gradient solitons of the RicciBourguignon flow. For this, we apply certain maximum principles based on the notions of convergence to zero at infinity, polynomial volume growth (both concerned with complete noncompact Riemannian manifolds), and stochastic completeness. A specific triviality result concerning complete noncompact gradient traceless Ricci solitons with nonnegative sectional curvature is also given.

引用

页码：89 / 98

页数：10

共 26 条

[1] A maximum principle at infinity with applications to geometric vector fields [J].

Alias, L. J. ;

Caminha, A. ;

do Nascimento, F. Y. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 474 (01) :242-247

[2]

Alias LJ., 2016, Maximum Principles and Geometric Applications, DOI [10.1007/978-3-319-24337-5, DOI 10.1007/978-3-319-24337-5]

[3] A maximum principle related to volume growth and applications [J].

Alias, Luis J. ;

Caminha, Antonio ;

do Nascimento, F. Yure .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2021, 200 (04) :1637-1650

[4]

[Anonymous], 1970, J. Differential Geom.

[5]

Bär C, 2010, P AM MATH SOC, V138, P2629

[6]

Bourguignon J.P., 1981, Lect. Notes Math., V838, P42

[7]

Cao H-D, 2010, Adv. Lect. Math. (ALM), V11, P1

[8] THE RICCI-BOURGUIGNON FLOW [J].

Catino, Giovanni ;

Cremaschi, Laura ;

Djadli, Zindine ;

Mantegazza, Carlo ;

Mazzieri, Lorenzo .

PACIFIC JOURNAL OF MATHEMATICS, 2017, 287 (02) :337-370

[9] Gradient Einstein solitons [J].

Catino, Giovanni ;

Mazzieri, Lorenzo .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 132 :66-94

[10] Rigidity of gradient Einstein shrinkers [J].

Catino, Giovanni ;

Mazzieri, Lorenzo ;

Mongodi, Samuele .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2015, 17 (06)

← 1 2 3 →