Geometry of manifolds which admit conservation laws
Annales de l'Institut Fourier, Volume 21 (1971) no. 1, p. 1-9

Let $M$ be an $\left(n+1\right)$-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.

Soit $M$ une variété riemannienne à $\left(n+1\right)$ 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.

@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},
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, Volume 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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