Geodesic
Geometry of fibered graphs of mappings
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Tome 179 (2020), pp. 50-59

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

In this paper, we examine the differential-geometric aspect of constant-rank mappings of smooth manifolds based on the concept of a graph as a smooth submanifold in the space of the direct product of the original manifolds. The nonmaximality of the rank provides the fibered nature of the graph. A Riemannian structure on manifolds enriches the geometry of the graph, which now essentially depends on the induced field of the metric tensor; we characterize relatively affine, projective, and $g$-umbilical mappings. The final part of the paper is devoted to mappings of Euclidean spaces of the types described earlier in terms of V. T. Bazylev's constructive graph.
Keywords: constant-rank mapping of manifolds, graph of a mapping, fibered submanifold, almost product structure, relatively affine mapping, $g$-umbilical mapping. 
@article{INTO_2020_179_a7,
     author = {A. A. Rylov},
     title = {Geometry of fibered graphs of mappings},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {50--59},
     publisher = {mathdoc},
     volume = {179},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_179_a7/}
}
TY  - JOUR
AU  - A. A. Rylov
TI  - Geometry of fibered graphs of mappings
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 50
EP  - 59
VL  - 179
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_179_a7/
LA  - ru
ID  - INTO_2020_179_a7
ER  - 
%0 Journal Article
%A A. A. Rylov
%T Geometry of fibered graphs of mappings
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 50-59
%V 179
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_179_a7/
%G ru
%F INTO_2020_179_a7
A. A. Rylov. Geometry of fibered graphs of mappings. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Tome 179 (2020), pp. 50-59. http://geodesic.mathdoc.fr/item/INTO_2020_179_a7/