Torse-forming vector fields in \(T\)-semisymmetric Riemannian spaces. (English) Zbl 0994.53009

Kozma, L. (ed.) et al., Steps in differential geometry. Proceedings of the colloquium on differential geometry, Debrecen, Hungary, July 25-30, 2000. Debrecen: Univ. Debrecen, Institute of Mathematics and Informatics, 219-229 (2001).
A Riemannian space \(V_n\) is called \(T\)-semisymmetric, where \(T\) is a tensor field on \(V_n\), if the curvature tensor field \(R\) satisfies the condition \(R(X,Y)\circ T=0\), for arbitrary vector fields \(X,Y\). A vector field \(\xi\) on \(V_n\) is called torse-forming if there are a function \(\rho\) and a 1-form \(\alpha\) so that \(\nabla_X\xi =\rho X+\alpha (X)\xi\). In this paper the authors establish some properties for torse-forming vectors fields in a \(T\)-semisymmetric Riemannian space, where \(T\) is 1-form, a 2-covariant tensor field or the Ricci tensor field of \(V_n\).
For the entire collection see [Zbl 0966.00031].
Reviewer: V.Cruceanu (Iaşi)


53B20 Local Riemannian geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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