We prove the following two new optimal immersion results for complex projective space. First, if n 3 mod 8 but n 6 3 mod 64, and (n) = 7, then CP can be immersed in R 4n 14 . Second, if n is even and (n) = 3, then CP can be immersed in R 4 . Here (n) denotes the number of 1's in the binary expansion of n. The rst contradicts a result of Crabb, which said that such an immersion does not exist, a...

We construct the action-angle variables of a classical integrable model defined on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase approximation. We show that the resulting expression for the propagator coincides with the exact propagator which was obtained by solving the time-dependent ...

We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space Fq(r, d) of singular foliations of codimension q and degree d on the complex projective space P , when 1 ≤ q ≤ r − 2. We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute the...

Abstract. In this paper we consider eigenvalues of Schrödinger operator with a weight on compact Riemannian manifolds with boundary (possibly empty) and prove a general inequality for them. By using this inequality, we study eigenvalues of Schrödinger operator with a weight on compact domains in a unit sphere, a complex projective space and a minimal submanifold in a Euclidean space. We also st...

1. The main results Let A be a hyperplane arrangement in the complex projective space P n , with n > 0.

We show how a ruled minimal Lagrangian submanifold of complex projective 3-space may be used to construct two related minimal surfaces in the 5-sphere.

We show that the efficiency of a natural pairing between certain projectively invariant Hardy spaces on dual strongly C-linearly convex real hypersurfaces in complex projective space is measured by the norm of the corresponding Leray transform.