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 RP^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).