Geometry of manifolds which admit conservation laws

Blair, David E., and Stone, Alexander P.. "Geometry of manifolds which admit conservation laws." Annales de l'institut Fourier 21.1 (1971): 1-9. <http://eudml.org/doc/74026>.

@article{Blair1971,
abstract = {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.},
author = {Blair, David E., Stone, Alexander P.},
journal = {Annales de l'institut Fourier},
keywords = {differential geometry},
language = {eng},
number = {1},
pages = {1-9},
publisher = {Association des Annales de l'Institut Fourier},
title = {Geometry of manifolds which admit conservation laws},
url = {http://eudml.org/doc/74026},
volume = {21},
year = {1971},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 1
SP - 1
EP - 9
AB - 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.
LA - eng
KW - differential geometry
UR - http://eudml.org/doc/74026
ER -