Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 33, No. 1, pp. 53-60 (2017)

On the concircular vector fields of spaces with affine connection

Irena Hinterleitner, Volodymyr Berezovski, Elena Chepurna and Josef Mikes

Brno University of Technology, Uman National University of Horticultur, Odessa State Economical University, Palacky University

Abstract: In this paper we study concircular vector fields of spaces with affine connection. We found the fundamental equation of these fields for the minimal requirements on the differentiability of the connection. The maximal numbers of linearly independent fields (with constant coefficients) is equal to $n+1$ and is realized only on projective flat spaces. Further we found a criterion on the Weyl tensor of the projective curvature of spaces, in which exist exactly $n-1$ independent concircular vector fields.

Keywords: concircular vector field, smoothness class, fundamental equation, manifold with affine connection

Classification (MSC2000): 53B20; 53B30, 53B35, 53B50

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