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.

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

In this note, we prove that the Witten genus of nonsingular stringy complete intersections in product of complex projective spaces vanishes.

The topological manifolds arising from configurations of points in the real and complex projective lines are classified. Their topology and combinatorics are described for the real case. A general setting for the study of the spaces of configurations of flats is established and a projective duality among them is proved in its full generality.

We give an elementary introduction to the first author’s theory of intersection spaces associated to complex projective varieties with only isolated singularities. We also survey recent results on the deformation invariance of intersection space homology in the context of projective hypersurfaces with an isolated singularity.

It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and fibrations. Endomorphisms of the projective spaces are also discussed and some results on invariant subvarieties under the pullback of the endomorphism are obt...

a module is said to be $pi$-extending provided that every projection invariant submodule is essential in a direct summand of the module. in this paper, we focus on direct summands and indecomposable decompositions of $pi$-extending modules. to this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.