The slices of a cone and a characterization of ellipsoids
Meyer, Mathieu ; Rogalski, M
HAL, hal-00693899 / Harvested from HAL
Text on HAL
Let C be a convex cone in R-d with non-empty interior and a compact basis K. If H-1 and H-2 are any two parallel hyperplanes tangent to K, whose slices with C are two other compact basis K-1 and K-2, let D, D-1 and D-2 be the truncated subcones of C generated by K, K-1 and K-2.(.) We prove that K is an ellipsoid if, and only if, vol (D)(2) = vol (D-1) vol (D-2) for every such pair of hyperplanes H-1 and H-2.
Publié le : 1998-07-05
Classification:  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{hal-00693899,
     author = {Meyer, Mathieu and Rogalski, M},
     title = {The slices of a cone and a characterization of ellipsoids},
     journal = {HAL},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00693899}
}

Meyer, Mathieu; Rogalski, M. The slices of a cone and a characterization of ellipsoids. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-00693899/