Electrostatic system with divergence-free Bach tensor and non-null cosmological constant
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Benedito Leandro
und
Róbson Lousa
Abstract
We prove that three-dimensional electrostatic manifolds with divergence-free Bach tensor are locally conformally flat, provided that the electric field and the gradient of the lapse function are linearly dependent. Consequently, a three-dimensional electrostatic manifold admits a local warped product structure with a one-dimensional base and a constant curvature surface fiber.
Funding source: Conselho Nacional de Desenvolvimento Científico e Tecnológico
Award Identifier / Grant number: 303157/2022-4
Award Identifier / Grant number: 403349/2021-4
Funding statement: Benedito Leandro was partially supported by CNPq/Brazil Grant 303157/2022-4. Róbson Lousa was partially supported by PROPG-CAPES [Finance Code 001]. The authors were partially supported by CNPq Grant 403349/2021-4.
Acknowledgements
The authors would like to express their gratitude to Professor Tiarlos Cruz for his valuable comments and insightful discussions. We also want to thank the referee for carefully reading this work and for the relevant remarks.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Open orbits and primitive zero ideals for solvable Lie algebras
- On the Pauli group on 2-qubits in dynamical systems with pseudofermions
- Electrostatic system with divergence-free Bach tensor and non-null cosmological constant
- Perturbation of domain for the linear parabolic equation
- K-theory of flag Bott manifolds
- Some results on Seshadri constants of vector bundles
- Strichartz inequality for orthonormal functions associated with special Hermite operator
- The globally smooth solutions and asymptotic behavior of the nonlinear wave equations in dimension one with multiple speeds
- On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems
- Boundedness of commutators of rough Hardy operators on grand variable Herz spaces
- Beurling densities of regular maximal orthogonal sets of self-similar spectral measure with consecutive digit sets
- An alternative proof of Tataru’s dispersive estimates
- The p-Bohr radius for vector-valued holomorphic and pluriharmonic functions
- Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction
- Decay and Strichartz estimates for Klein–Gordon equation on a cone I: Spinless case
- A class of quaternionic Fourier orthonormal bases
- Maximal estimates for fractional Schrödinger equations in scaling critical magnetic fields
- Normalized solutions for scalar field equation involving multiple critical nonlinearities
Artikel in diesem Heft
- Frontmatter
- Open orbits and primitive zero ideals for solvable Lie algebras
- On the Pauli group on 2-qubits in dynamical systems with pseudofermions
- Electrostatic system with divergence-free Bach tensor and non-null cosmological constant
- Perturbation of domain for the linear parabolic equation
- K-theory of flag Bott manifolds
- Some results on Seshadri constants of vector bundles
- Strichartz inequality for orthonormal functions associated with special Hermite operator
- The globally smooth solutions and asymptotic behavior of the nonlinear wave equations in dimension one with multiple speeds
- On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems
- Boundedness of commutators of rough Hardy operators on grand variable Herz spaces
- Beurling densities of regular maximal orthogonal sets of self-similar spectral measure with consecutive digit sets
- An alternative proof of Tataru’s dispersive estimates
- The p-Bohr radius for vector-valued holomorphic and pluriharmonic functions
- Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction
- Decay and Strichartz estimates for Klein–Gordon equation on a cone I: Spinless case
- A class of quaternionic Fourier orthonormal bases
- Maximal estimates for fractional Schrödinger equations in scaling critical magnetic fields
- Normalized solutions for scalar field equation involving multiple critical nonlinearities
