Conformally geodesic mappings satisfying a certain initial condition. (English) Zbl 1265.53019

Chudá, Hana; Mikeš, Josef

Arch. Math., Brno 47, No. 5, 389-394 (2011).

In the article, so-called conformally geodesic mappings are studied. The authors investigate conditions under which a conformally geodesic mapping is conformal. More precisely, they prove that a conformally geodesic mapping is conformal if the Weyl curvature tensor field does not vanish. In a sense they prove that a conformally geodesic mapping must be conformal if the manifold is “sufficiently asymmetric”. The methods used are based on the so called Levi-Civita equation.

Reviewer: Martin Čadek (Brno)

MSC:

53B20	Local Riemannian geometry
53B30	Local differential geometry of Lorentz metrics, indefinite metrics
53C21	Methods of global Riemannian geometry, including PDE methods; curvature restrictions

Keywords:

conformal mapping; geodesic mapping; conformally geodesic mapping