Extension of a Riemannian metric with vanishing curvature
Mardare, Cristinel ; Ciarlet, Philippe G.
HAL, hal-00018093 / Harvested from HAL
Text on HAL
Let Ω be a connected and simply-connected open subset of R^n such that the geodesic distance in Ω is equivalent to the Euclidean distance. Let there be given a Riemannian metric (g_{ij}) of class C^2 and of vanishing curvature in Ω, such that the functions g_{ij} and their partial derivatives of order ≤ 2 have continuous extensions to Ω. Then there exists a connected open subset Ω' of Rn containing Ω and a Riemannian metric (g'_{ij}) of class C^2 and of vanishing curvature in Ω' that extends the metric (g_{ij}).
Publié le : 2004-07-05
Classification:  Fundamental theorem of Riemannian geometry,  extension of metrics,  [MATH]Mathematics [math],  [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA],  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{hal-00018093,
     author = {Mardare, Cristinel and Ciarlet, Philippe G. },
     title = {Extension of a Riemannian metric with vanishing curvature},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00018093}
}

Mardare, Cristinel; Ciarlet, Philippe G. . Extension of a Riemannian metric with vanishing curvature. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00018093/