Geodesic
Grassman image of non-isotropic surface of pseudo-euclidean space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 65-75.

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

We consider submanifolds of non-isotropic planes of the Grassman manifold of the pseudo-Euclidean space. We prove a theorem about the unboundedness of the sectional curvature of the submanifolds of the two-dimensional non-isotropic planes of the four-dimensional pseudo-Euclidean space with the help of immersion in the six-dimensional pseudo-Euclidean space of index 3. We also introduce a concept of the indicatrix of normal curvature and study the properties of this indicatrix and the Grassman image of the non-isotropic surface of the pseudo-Euclidean space. We find a connection between the curvature of the Grassman image and the intrinsic geometry of the plane. We suggest the classification of the points of the Grassman image.
Keywords: pseudo-Euclidean space, Grassman manifold, sectional curvature, Grassman image of the surface, indicatrix of the normal curvature. 
@article{IVM_2017_2_a6,
     author = {P. G. Stegantseva and M. A. Grechneva},
     title = {Grassman image of non-isotropic surface of pseudo-euclidean space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {65--75},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_2_a6/}
}
TY  - JOUR
AU  - P. G. Stegantseva
AU  - M. A. Grechneva
TI  - Grassman image of non-isotropic surface of pseudo-euclidean space
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 65
EP  - 75
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_2_a6/
LA  - ru
ID  - IVM_2017_2_a6
ER  - 
%0 Journal Article
%A P. G. Stegantseva
%A M. A. Grechneva
%T Grassman image of non-isotropic surface of pseudo-euclidean space
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 65-75
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_2_a6/
%G ru
%F IVM_2017_2_a6
P. G. Stegantseva; M. A. Grechneva. Grassman image of non-isotropic surface of pseudo-euclidean space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 65-75. http://geodesic.mathdoc.fr/item/IVM_2017_2_a6/

[1] Aminov Yu. A., Geometriya podmnogoobrazii, Nauk. dumka, Kiev, 2002

[2] Borisenko A. A., Nikolaevskii Yu. A., “Mnogoobraziya Grassmana i grassmanov obraz podmnogoobrazii”, UMN, 46:2 (1991), 41–80 | MR | Zbl

[3] Gurgenidze M. A., Stegantseva P. G., “Vnutrennyaya geometriya grassmanova mnogoobraziya psevdoevklidova prostranstva”, Visnik Kharkivsk. nats. un-tu. Ser. Matem., prikl. matem. i mekhan., 826:58 (2008), 141–150 | Zbl

[4] Gurgenidze M. A., “O pogruzhenii grassmanova mnogoobraziya psevdoevklidova prostranstva”, Zbirnik prats In-tu matem. NAN Ukraïni, 3:3 (2006), 107–114

[5] Rozenfeld B. A., Mnogomernye prostranstva, Nauka, M., 1966

[6] Wong Y. C., “Differential geometry of Grassman manifolds”, Proc. Math. Acad. Sci. USA, 1967, 589–594 | DOI | MR | Zbl

[7] Eizenkhart L. P., Rimanova geometriya, In. lit., M., 1948

[8] Gorokh V. P., “O dvumernykh minimalnykh poverkhnostyakh v psevdoevklidovom prostranstve”, Ukr. geometrich. sb., 31 (1988), 36–47 | MR | Zbl