Geodesic
Totally geodesic subsets in the variety of directions of physical space
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 141-153

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $M_0$ be a Minkowski 4-spase, $\Lambda_2(M_0)$ its second exterior power equipped with a structure of pseudo-Euclidean space with singature $(3,3)$, $K_0(M_0)$ the light cone, $G_1\subset\Lambda_2(M_0)$ the set of oriented 2-planes meeting the interior of $K_0(M_0)$. In the paper, 4 types of totally geodesic two-manifolds in $G_1$ are discribed, such that manifolds of one type are pairwise congruent as subsets in $\Lambda_2(M_0)$, while mainfolds of different types are not. Models of such mainfolds in the disk $D^3$ are constructed. An explicit formula for the curvature of $G_1$ is given. 
@article{ZNSL_2001_279_a7,
     author = {D. V. Ivanov},
     title = {Totally geodesic subsets in the variety of directions of physical space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {141--153},
     publisher = {mathdoc},
     volume = {279},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a7/}
}
TY  - JOUR
AU  - D. V. Ivanov
TI  - Totally geodesic subsets in the variety of directions of physical space
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2001
SP  - 141
EP  - 153
VL  - 279
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a7/
LA  - ru
ID  - ZNSL_2001_279_a7
ER  - 
%0 Journal Article
%A D. V. Ivanov
%T Totally geodesic subsets in the variety of directions of physical space
%J Zapiski Nauchnykh Seminarov POMI
%D 2001
%P 141-153
%V 279
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a7/
%G ru
%F ZNSL_2001_279_a7
D. V. Ivanov. Totally geodesic subsets in the variety of directions of physical space. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 141-153. http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a7/