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

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
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