01285nas a2200097 4500008004300000245007100043210006700114520095200181100001801133856003601151 2006 en_Ud 00aFundamental form and Cartan tensor of (2,5)-distributions coincide0 aFundamental form and Cartan tensor of 25distributions coincide3 aIn our previous paper for generic rank 2 vector distributions on n-dimensional manifold (n greater or equal to 5) we constructed a special differential invariant, the fundamental form. In the case n=5 this differential invariant has the same algebraic nature, as the covariant binary biquadratic form, constructed by E.Cartan in 1910, using his ``reduction- prolongation\\\'\\\' procedure (we call this form Cartan\\\'s tensor). In the present paper we prove that our fundamental form coincides (up to constant factor -35) with Cartan\\\'s tensor. This result explains geometric reason for existence of Cartan\\\'s tensor (originally this tensor was obtained by very sophisticated algebraic manipulations) and gives the true analogs of this tensor in Riemannian geometry. In addition, as a part of the proof, we obtain a new useful formula for Cartan\\\'s tensor in terms of structural functions of any frame naturally adapted to the distribution.1 aZelenko, Igor uhttp://hdl.handle.net/1963/2187