Calvo, Maria del Carmen; Keilhauer, Guillermo G. R. Tensor fields of type \((0,2)\) on the tangent bundle of a Riemannian manifold. (English) Zbl 0921.53013 Geom. Dedicata 71, No. 2, 209-219 (1998). The authors associate a global matrix function to every \((0,2)\)-tensor field on the tangent bundle TM of a Riemannian manifold \(M\). This enables them to characterize, in an original way, the natural \((0,2)\)-tensor fields on \(M\) constructed by O. Kowalski and M. Sekizawa [Bull. Tokyo Gakugei Univ., Sect. IV, Ser. Math. Nat. Sci. 40, 1-29 (1988; Zbl 0656.53021)] and J. Janyška [Suppl. Rend. Circ. Mat. Palermo, II. Ser. 32, 165-174 (1994; Zbl 0818.53020)]. Reviewer: I.Kolář (Brno) Cited in 3 Documents MSC: 53C20 Global Riemannian geometry, including pinching 53B21 Methods of local Riemannian geometry 53A55 Differential invariants (local theory), geometric objects Keywords:connection; \((0,2)\)-tensor field; tangent bundle; Riemannian manifold Citations:Zbl 0656.53021; Zbl 0818.53020 PDF BibTeX XML Cite \textit{M. d. C. Calvo} and \textit{G. G. R. Keilhauer}, Geom. Dedicata 71, No. 2, 209--219 (1998; Zbl 0921.53013) Full Text: DOI OpenURL