We explicitly construct the twistor spaces of Joyce metrics with torus action that are not treated in Part I. This finishes a construction of all the twistor spaces of Joyce metrics on the connected sum of four complex projective planes.

A bstract We introduce a generic procedure to reduce supersymmetric Yang-Mills (SYM) theory along the Hopf fiber of squashed S 2 r− 1 with U(1) r isometry, down ℂℙ base. This amounts fixing Killing vector v generating ⊂ rotation and dimensionally reducing either or another direction contained in . To perform such reduction we ℤ p quotient freely acting one two fibers. For fixed resulting manifo...

Let M2n be an oriented closed smooth manifold homotopy equivalent to the complex projective space CP(n). The main purpose of this paper is show that when n even, difference between first Pontrjagin class and CP(n) divisible by 16. As a geometric application result, we prove Kervaire sphere dimension 4k+1 does not admit any free circle group action if k+1 power 2.