Let be an -dimensional Riemannian manifold admitting a covariant constant endomorphism of the localized module of 1-forms with distinct non-zero eigenvalues. After it is shown that is locally flat, a manifold immersed in is studied. The manifold has an induced structure with of the same eigenvalues if and only if the normal to is a fixed direction of . Finally conditions under which is invariant under , is totally geodesic and the induced structure has vanishing Nijenhuis torsion or is covariant constant are found.
Soit une variété riemannienne à dimensions, admettant un endomorphisme covariant constant du module local de 1-formes ayant des valeurs propres distinctes et différentes de zéro. On montre que est localement plat, et on étudie une variété immergée dans . La variété a une structure induite avec des mêmes valeurs propres si et seulement si la normale à est une direction fixe de . Enfin, on trouve les conditions sous lesquelles est invariant sous , 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}, pages = {1--9}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {21}, number = {1}, year = {1971}, doi = {10.5802/aif.359}, zbl = {0197.18101}, mrnumber = {44 #948}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.359/} }
TY - JOUR AU - Blair, David E. AU - Stone, Alexander P. TI - Geometry of manifolds which admit conservation laws JO - Annales de l'Institut Fourier PY - 1971 SP - 1 EP - 9 VL - 21 IS - 1 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.359/ DO - 10.5802/aif.359 LA - en ID - AIF_1971__21_1_1_0 ER -
%0 Journal Article %A Blair, David E. %A Stone, Alexander P. %T Geometry of manifolds which admit conservation laws %J Annales de l'Institut Fourier %D 1971 %P 1-9 %V 21 %N 1 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.359/ %R 10.5802/aif.359 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.359/
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