On the geometric behavior of Cotton solitons immersed in certain classes of GRW spacetimes

Giovanni Molica Bisci; Henrique F. de Lima; Ary V. F. Leite; Marco A. L. Velásquez; Giovanni Molica Bisci; Henrique F. de Lima; Ary V. F. Leite; Marco A. L. Velásquez

doi:10.3934/era.2026073

Electronic Research Archive

2026, Volume 34, Issue 3: 1609-1625. doi: 10.3934/era.2026073

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On the geometric behavior of Cotton solitons immersed in certain classes of GRW spacetimes

1.
Department of Human Sciences and Quality of Life Promotion, University San Raffaele Roma, 00166 Roma, Italy
2.
Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Paraíba, Brazil

Received: 31 October 2025 Revised: 01 February 2026 Accepted: 03 February 2026 Published: 27 February 2026

In the present manuscript, we investigate the geometric behavior of complete and stochastically complete Cotton solitons isometrically immersed in a generalized Robertson-Walker (GRW) spacetime whose sectional curvature of the Riemannian fiber satisfies suitable curvature constraints. In this configuration, by assuming appropriate hypotheses on the warped structure of the GRW spacetime, we jointly use a Bochner-type formula with several maximum principles, integrability conditions, and a parabolicity criterion in order to show that such a Cotton soliton must be trivial and locally conformally flat. Additionally, applications of our main results for the steady state space, the de Sitter space, the future temporal cone of the Lorentz-Minkowski space, and a specific open subset of the anti-de Sitter space are also presented.
Citation: Giovanni Molica Bisci, Henrique F. de Lima, Ary V. F. Leite, Marco A. L. Velásquez. On the geometric behavior of Cotton solitons immersed in certain classes of GRW spacetimes[J]. Electronic Research Archive, 2026, 34(3): 1609-1625. doi: 10.3934/era.2026073

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Abstract

In the present manuscript, we investigate the geometric behavior of complete and stochastically complete Cotton solitons isometrically immersed in a generalized Robertson-Walker (GRW) spacetime whose sectional curvature of the Riemannian fiber satisfies suitable curvature constraints. In this configuration, by assuming appropriate hypotheses on the warped structure of the GRW spacetime, we jointly use a Bochner-type formula with several maximum principles, integrability conditions, and a parabolicity criterion in order to show that such a Cotton soliton must be trivial and locally conformally flat. Additionally, applications of our main results for the steady state space, the de Sitter space, the future temporal cone of the Lorentz-Minkowski space, and a specific open subset of the anti-de Sitter space are also presented.

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