On warped product gradient η-Ricci solitons Article Swipe

PDF

Related Concepts

Mathematics Scalar curvature Conservative vector field Soliton Vector field Ricci curvature Mathematical analysis Mathematical physics Manifold (fluid mechanics) Scalar (mathematics) Curvature Curvature of Riemannian manifolds Product (mathematics) Pure mathematics Nonlinear system Sectional curvature Physics Geometry Quantum mechanics Thermodynamics Engineering Mechanical engineering Compressibility

Adara M. Blaga ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.2298/fil1718791b · OA: W2964047378

If the potential vector field of an ?-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a nonlinear second order PDE. In a particular case of irrotational potential vector field we prove that the soliton is completely determined by f . We give a way to construct a gradient ?-Ricci soliton on a warped product manifold and show that if the base manifold is oriented, compact and of constant scalar curvature, the soliton on the product manifold gives a lower bound for its scalar curvature.