Tensor fields of type \((0,2)\) on the tangent bundle of a Riemannian manifold. (English) Zbl 0921.53013

Calvo, Maria del Carmen; Keilhauer, Guillermo G. R.

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)

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