1. Throughout P = C ∪ {∞} denotes the Riemann sphere, H denotes the upper half plane, C∗ denotes the multiplicative group of complex numbers, and P = (C \ {0})/C∗ denotes n dimensional complex projective space. For w ∈ C \{0} let [w] := wC∗ denote the corresponding point of P. For A ∈ GLn+1(C) let MA denote the corresponding automorphism of projective space so that MA([w]) = [Aw]. Identify P an...

fibre is the re-dimensional complex projective space (complex projective co-tangent bundle). This bundle of complex dimension 2re + l is our M. Considering the fibre of T(V) as the (2w+2)-dimensional real vector space, we take as P the co-tangent sphere bundle over V (i.e., the fibre of P is a sphere in the fibre of T(V)). T(V) — V is the principal fibre bundle associated with a line bundle L o...

In this paper we obtain the conditions in which two complex Finsler metrics are projective, i.e. have the same geodesics as point sets. Two important classes of such metrics are submitted to our attention: conformal projective and weakly projective complex Finsler spaces. For each of them we study the transformations of the canonical connection. We pay attention for local projectivity with a pu...

It is shown that all but at most countably many spaces in the genus of HP∞, the infinite quaternionic projective space, do not admit any essential maps from CP∞, the infinite complex projective space. This strengthens a theorem of McGibbon and Rector which states that among the uncountably many homotopy types in its genus, HP∞ is the only one which admits a maximal torus.

In this paper, we determine the total Stiefel-Whitney classes of vector bundles over the product of the complex projective space CP (j) with the quaternionic projective space HP (k). Moreover, we show that every involution fixing CP (2m+1)×HP (k) bounds. AMS subject classifications: 57R85, 57S17, 55N22

We prove that for every positive integer m ≥ 18(2 · 3)! and every smooth projective 3-fold of general type X defined over complex numbers, | mKX | gives a birational rational map from X into a projective space.

We give an elementary explicit construction of cell decomposition of the mod-uli space of projective structures on a two dimensional surface, analogous to the decomposition of Penner/Strebel for moduli space of complex structures. The relations between projective structures and P GL(2, C) flat connections are also described.

We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a " hyperbolic non-percolation " property. We use this method to show that general small deformations of certain singular abelian surfaces of degree 8 are hyperbolic. We also show that a union of 15 planes in general position in projective 3-space admits hyperbol...

We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a “hyperbolic non-percolation” property. We use this method to show that general small deformations of certain singular abelian surfaces of degree 8 are hyperbolic. We also show that a union of 15 planes in general position in projective 3-space admits hyperbolic...