The single-leaf Frobenius Theorem with Applications
| dc.creator | Piccione, Paolo | |
| dc.creator | Tausk, Daniel V. | |
| dc.date | 2005-10-26 | |
| dc.date.accessioned | 2026-07-07T06:47:55Z | |
| dc.date.available | 2026-07-07T06:47:55Z | |
| dc.description | Using the notion of Levi form of a smooth distribution, we discuss the local and the global problem of existence of one horizontal section of a smooth vector bundle endowed with a horizontal distribution. The analysis will lead to the formulation of a "one-leaf" analogue of the classical Frobenius integrability theorem in elementary differential geometry. Several applications of the result will be discussed. First, we will give a characterization of symmetric connections arising as Levi-Civita connections of semi-Riemannian metric tensors. Second, we will prove a general version of the classical Cartan-Ambrose-Hicks Theorem giving conditions on the existence of an affine map with prescribed differential at one point between manifolds endowed with connections. | |
| dc.description | 39 pages, no figure | |
| dc.identifier | https://arxiv.org/abs/math/0510555 | |
| dc.identifier | http://arxiv.org/abs/math/0510555 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103815 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B05; 53C05; 53C42; 55R25 | |
| dc.title | The single-leaf Frobenius Theorem with Applications | |
| dc.type | text |