Geometry of manifolds which admit conservation laws
Annales de l'Institut Fourier, Tome 21 (1971) no. 1, p. 1-9
Soit M une variété riemannienne à (n+1) dimensions, admettant un endomorphisme covariant constant h du module local de 1-formes ayant des valeurs propres distinctes et différentes de zéro. On montre que M est localement plat, et on étudie une variété N immergée dans M. La variété N a une structure induite avec n des mêmes valeurs propres si et seulement si la normale à N est une direction fixe de h. Enfin, on trouve les conditions sous lesquelles N est invariant sous h, N est totalement géodésique et la structure induite a une torsion de Nijenhuis nulle ou est covariante constante.
Let M be an (n+1)-dimensional Riemannian manifold admitting a covariant constant endomorphism h of the localized module of 1-forms with distinct non-zero eigenvalues. After it is shown that M is locally flat, a manifold N immersed in M is studied. The manifold N has an induced structure with n of the same eigenvalues if and only if the normal to N is a fixed direction of h. Finally conditions under which N is invariant under h, N is totally geodesic and the induced structure has vanishing Nijenhuis torsion or is covariant constant are found.
@article{AIF_1971__21_1_1_0,
     author = {Blair, David E. and Stone, Alexander P.},
     title = {Geometry of manifolds which admit conservation laws},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {21},
     number = {1},
     year = {1971},
     pages = {1-9},
     doi = {10.5802/aif.359},
     zbl = {0197.18101},
     mrnumber = {44 \#948},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1971__21_1_1_0}
}
Blair, David E.; Stone, Alexander P. Geometry of manifolds which admit conservation laws. Annales de l'Institut Fourier, Tome 21 (1971) no. 1, pp. 1-9. doi : 10.5802/aif.359. http://www.numdam.org/item/AIF_1971__21_1_1_0/

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