Giovanni Molica Bisci†, Henrique Fernandes de Lima‡ , Ary Vinicius Ferreira Leite§ , Marco Antonio Lazaro Velasquez¶
Abstract: The purpose of our paper is to investigate the geometric behavior of complete noncompact and stochastically complete quasi k-Yamabe gra- dient solitons under appropriate conditions in order to obtain new triv- iality and nonexistence results. For this, we derive a suitable Bochner type formula and we apply it jointly with integrability criteria, Liou- ville type results and several maximum principles dealing, in particular, with the notion of convergence to zero at infinity and the concept of polynomial and exponential volume growth.
Keywords: complete and stochastically complete quasi k-Yamabe gradient solitons, σk-curvature, convergence to zero at infinity, polynomial and exponential volume growth.
MSC: 53C21, 53C24, 53C25.
DOI 10.56082/annalsarscimath.2025.3.387
† giovanni.molicabisci@uniroma5.it, Department of Human Sciences and Quality of Life Promotion, San Raffaele University of Rome, Rome, Italy
‡ henriquedelima74@gmail.com, Departamento de Matematica, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Paraıba, Brazil
§ ry.v.l.f@gmail.com, Departamento de Matematica, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Parıba, Brazil¶
¶ marcolazarovelasquez@gmail.com, Departamento de Matematica, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Paraıba, Brazil
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 3, 2025
