Detail publikace

On the geometry in the large of Einstein-like manifolds

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

Originální název

On the geometry in the large of Einstein-like manifolds

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

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

Vydáno

24. 6. 2022

Nakladatel

MDPI

Místo

Basel

ISSN

2227-7390

Periodikum

Mathematics

Ročník

2208

Číslo

1

Stát

Švýcarská konfederace

Strany od

2208-01

Strany do

2208-10

Strany počet

10

URL