Back to Search
Start Over
Geometry of Fibered Graphs of Mappings.
- Source :
-
Journal of Mathematical Sciences . Nov2023, Vol. 276 Issue 3, p400-409. 10p. - Publication Year :
- 2023
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RIEMANNIAN manifolds
*TENSOR fields
*GEOMETRY
Subjects
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 276
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 173517014
- Full Text :
- https://doi.org/10.1007/s10958-023-06756-9