On the geometry in the large of Einstein-like manifolds

On the geometry in the large of Einstein-like manifolds

WoS Article

Gray has presented the invariant orthogonal irreducible decomposition of the space of all covariant tensors of rank 3, obeying only the identities of the gradient of the Ricci tensor. This decomposition introduced the seven classes of Einstein-like manifolds, the Ricci tensors of which fulfill the defining condition of each subspace. The large-scale geometry of such manifolds has been studied by many geometers using the classical Bochner technique. However, the scope of this method is limited to compact Riemannian manifolds. In the present paper, we prove several Liouville-type theorems for certain classes of Einstein-like complete manifolds. This represents an illustration of the new possibilities of geometric analysis.

Gray has presented the invariant orthogonal irreducible decomposition of the space of all covariant tensors of rank 3, obeying only the identities of the gradient of the Ricci tensor. This decomposition introduced the seven classes of Einstein-like manifolds, the Ricci tensors of which fulfill the defining condition of each subspace. The large-scale geometry of such manifolds has been studied by many geometers using the classical Bochner technique. However, the scope of this method is limited to compact Riemannian manifolds. In the present paper, we prove several Liouville-type theorems for certain classes of Einstein-like complete manifolds. This represents an illustration of the new possibilities of geometric analysis.

Einstein-like manifold; Bochner method; Sampson Laplacian; Bourguignon Laplacian; vanishing theorem

Einstein-like manifold; Bochner method; Sampson Laplacian; Bourguignon Laplacian; vanishing theorem

MIKEŠ, J.; RÝPAROVÁ, L.; STEPANOV, S.; TSYGANOK, I.

2023

24.06.2022

MDPI

Basel

2227-7390

Mathematics

2208

1

Swiss Confederation

2208-01

2208-10

10

https://www.mdpi.com/2227-7390/10/13/2208