Giovanni Molica Bisci†, Henrique Fernandes de Lima‡ , Ary Vinicius Ferreira Leite§ , Marco Antonio Lázaro Velásquez¶
Abstract: The purpose of our paper is to investigate the geometric behavior of complete noncompact and stochastically complete quasi k-Yamabe gradient solitons under appropriate conditions in order to obtain new triviality and nonexistence results. For this, we derive a suitable Bochner type formula and we apply it jointly with integrability criteria, Liouville 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
