We introduce a generalization to the second order of the notion of the G1-structure, the so called generalized almost tangent structure. For this purpose, the concepts of the second order frame bundle H2(Vm), its structural group Lm 2 and its associated tangent bundle of second order T2(Vm) of a differentiable manifold Vm are described from the point of view that is used. Then, a G1-structure of second order -called G1 2-structure- is constructed on Vm by an endorphism J acting on T2(Vm), satisfying the relation J2 = 0 and some hypothesis on its rank. Its connection and characteristic cohomology class are defined.
@article{urn:eudml:doc:41168,
title = {G1-structures of second order.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {51-64},
zbl = {0755.53022},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41168}
}
Demetropoulou Psomopoulou, Demetra. G1-structures of second order.. Publicacions Matemàtiques, Tome 36 (1992) pp. 51-64. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41168/