The object of the present paper is to study the totally umbilical hypersurfaces of weakly projective symmetric spaces and it is shown that the totally umbilical hypersurfaces of weakly projective symmetric space is also a weakly projective symmetric space.

In this paper we study the Cauchy–Riemann equation in complex projective spaces. Specifically, we use the modified weight function method to study the ∂̄-Neumann problem on pseudoconvex domains in these spaces. The solutions are used to study function theory on pseudoconvex domains via the ∂̄-Cauchy problem. We apply our results to prove nonexistence of Lipschitz Levi-flat hypersurfaces in comple...

We introduce new concepts of functional analysis: Hausdorff spectrum and Hausdorff limit or H-limit of Hausdorff spectrum of locally convex spaces. Particular cases of regular H-limit are projective and inductive limits of separated locally convex spaces. The class of H-spaces contains Fréchet spaces and is stable under forming countable inductive and projective limits, closed subspaces and quo...

Let P be a polar space induced by a quasipolarity on a projective space G. In this article, we give sufficient conditions for an embedding (i.e. an incidence-preserving map which is injective on points and lines) of P into a projective space H to be extendable to an incidencepreserving map from G to H. As a consequence, we obtain conditions for such an embedding to be induced by a semilinear ma...

We extend a result of to Esnault-Levine-Viehweg concerning the Chow groups of hypersurfaces in projective space to those in weighted projective spaces.

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. It was already shown in [1] that the inclusion of the first space into the second one is a homotopy equivalence. In this paper we prove that the homotopy types of the terms of the natural ‘degree’ filtration approximate closer and closer the homotopy type of the space o...

Given a manifold X , the set of manifold structures on X × ∆ relative to the boundary can be viewed as the k-th homotopy group of a space S̃s(X). This space is called the block structure space of X . Free involutions on spheres are in one-to-one correspondence with manifold structures on real projective spaces. We generalize Wall’s join construction for free involutions on spheres to define a fu...

We provide a simple algebraic construction of the twistor spaces of arbitrary Joyce’s self-dual metrics on the 4-manifold H 2 × T 2 that extend smoothly to nCP, the connected sum of complex projective planes. Indeed, we explicitly realize projective models of the twistor spaces of arbitrary Joyce metrics on nCP in a CP-bundle over CP, and show that they contain the twistor spaces of H 2 × T 2 a...

The linear code Cs,t(n, q) of s-spaces and t-spaces in a projective space PG(n, q), q = ph, p prime, is defined as the vector space spanned over Fp by the rows of the incidence matrix of s-spaces and t-spaces. This code generalises the code of points and lines in a projective plane, which has been intensively studied since the 1970’s. In this paper, we give an overview of what is currently know...