ИСТИНА

B.J.Sanderson noted that for k<n the projective space RP^k is immersible in R^n if and only if the tangent bundle TRP^n admits k linearly independent vector fields over RP^k [1, Lemma (9.7)]. Using this remark, P.F.Baum and W.Browder proved that RP^{10} can not be immersed to R^{15} [1, Corollary (9.9)] by showing that the tangent bundle TRP^{15} does not admit 9 linearly independent vector fields over RP^{10} [1, Thm. (9.5)]. We present a new proof of this last statement based on U.Koschorke' singularity approach [2]. References [1] P.F.Baum, W.Browder. The cohomology of quotients of classical groups // Topology 3 (1965), 305--336. [2] U.Koschorke. Vector Fields and Other Vector Bundle Morphisms - A Singularity Approach. Lecture Notes in Math. 847 (Springer, Berlin, 1981).