Abstract
We study generalized quasi-Einstein manifolds, or briefly, GQE manifolds. Here, we present relations between the Bach, Cotton and D tensors on GQE manifolds. Next, a 3-tensor E which measures the deviation of m-quasi-Einstein manifolds from GQE manifolds is introduced. Among others in dimension 3, it is shown that Bach-flatness implies locally conformally flatness. Furthermore, it is proved that, around a regular point of the fourth-order divergence free Weyl tensor, a GQE manifold is a locally warped product manifold with
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Meromorphic function sharing a small function with a homogeneous differential polynomial
- On generalized quasi-Einstein manifolds
- On Green’s function of the Robin problem for the Poisson equation
- Moment functions on hypergroup joins
- Sparse reconstruction with multiple Walsh matrices
- On certain equations in semiprime rings and standard operator algebras
- Derivatives of meromorphic functions sharing two sets with least cardinalities
- The metric derivative of set-valued functions
- The relativistic Enskog equation near the vacuum in the Robertson–Walker space-time
Articles in the same Issue
- Frontmatter
- Meromorphic function sharing a small function with a homogeneous differential polynomial
- On generalized quasi-Einstein manifolds
- On Green’s function of the Robin problem for the Poisson equation
- Moment functions on hypergroup joins
- Sparse reconstruction with multiple Walsh matrices
- On certain equations in semiprime rings and standard operator algebras
- Derivatives of meromorphic functions sharing two sets with least cardinalities
- The metric derivative of set-valued functions
- The relativistic Enskog equation near the vacuum in the Robertson–Walker space-time