Naslov
Generalizations of Killing vector fields in Sol space

Autori
Erjavec, Zlatko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Abstracts of 22nd Scientific-Professional Colloquium on Geometry and Graphics / Došlić, T. ; Jurkin, E. - Zagreb : Hrvatsko društvo za geometriju i grafiku, 2021, 16-16

Skup
22nd Scientific-Professional Colloquium on Geometry and Graphics

Mjesto i datum
Čiovo, Hrvatska, 05.09.2021. - 09.09.2021

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Killing vector field ; Sol space ; conformal vector field ; Lie derivative

Sažetak
Killing vector field on Riemannian manifold is a vector field X which satisfies the Killing equation L_{;X};g=0, where L denotes a Lie derivative. The Killing equation expresses that a metric of Riemannian manifold is invariant under the vector field X. Killing vector field flows preserve shapes and sizes and they are manifestations of symmetries in the context of general relativity. We consider the generalizations of the Killing vector fields in the 3D Sol space. Conformal Killing vector fields are the first generalization. They are defined by the conformal Killing equation L_{;X};g=\lambda g, where \lambda is a smooth function on M. 2-Killing vector fields defined by the 2-Killing equation L_{;X};(L_{;X};g)=0 are the second generalization. We characterize proper conformal Killing vector fields and determine some proper 2-Killing vector fields in Sol space. It seems that there are no proper conformal Killing vector field in Sol space. On the other hand, we explore the proper 2-Killing vector fields in Sol space and it seems that the approach used here can be starting point for classification of 2-Killing vector fields in other 3D homogeneous Riemannian geometries.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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