# zbMATH — the first resource for mathematics

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)

##### MSC:
 53B20 Local Riemannian geometry 53B30 Local differential geometry of Lorentz metrics, indefinite metrics
Full Text: