Non-extendibility of Tangent Bundles of Complex Projective Spaces and Quaternion Projective Spaces

1 Introduction Let K be a CW-complex and L be its subcomplex. A real (resp. complex) vector bundle over L is said to be extendible to K if it is equivalent to the restriction of a real (resp. complex) vector bundle over K. R. L. E. Schwarzenberger studied the non-extendibility of vector bundles over CP~n (resp. RP~n) to CP~m(resp. RP~m), m>n, where CP~n (resp. RP~n) is the complex (resp. real)