Geodesic
Nonlinear $m^p$-connectivities in principal fibrations
Matematičeskie zametki, Tome 11 (1972) no. 3, pp. 341-351.

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The paper deals with the multidimensional analog of the concept of nonlinear connectivity of order $p$, the content of the analog being that, for each $m$-submanifold of the basis of the principal fibration, there is defined a linear connectivity with horizontal $m$-distribution in the submanifolds passing through the common $m^p$-element of tangency. It has been possible to reduce consideration to the case of a linear connectivity in the appropriately chosen principal fibration. 
@article{MZM_1972_11_3_a13,
     author = {L. E. Evtushik},
     title = {Nonlinear $m^p$-connectivities in principal fibrations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {341--351},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_3_a13/}
}
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L. E. Evtushik. Nonlinear $m^p$-connectivities in principal fibrations. Matematičeskie zametki, Tome 11 (1972) no. 3, pp. 341-351. http://geodesic.mathdoc.fr/item/MZM_1972_11_3_a13/