In this paper we investigate the ergodic properties of a positive linear operator on a vector lattice of real-valued measurable functions on a sigma-finite measure space. Some results of Ornstein and Brunel are unified and improved.
We study the Mordell-Weil lattices of elliptic fibrations with sections on algebraic surfaces over complex numbers. In this paper, we obtain the minimum of the height pairing of such fibrations on K3 surfaces.
We show that any K-contact 3-structure on a 7-dimensional Riemannian manifold is a Sasakian 3-structure. By this we see that Konishi's construction of a 3-Sasakian manifold over a quaternionic Kähler manifold works for dimension≥4. We also study the case of quaternionic Kähler manifolds of negative scalar curvature by defining a triple of K-contact structures of nS-type.
We show that the Bergman kernel function, associated to pseudoconvex domains of finite type with the property that the Levi form of the boundary has at most one degenerate eigenvalue, is a standard kernel of Calderón-Zygmund type with respect to the Lebesgue measure. As an application, we show that the Bergman projection on these domains preserves some of the Lebesgue classes.
We construct a one-to-one correspondence between the equivariant diffeomorphism classes of smooth Sp(2, R)-actions on the standard 4-sphere without fixed points and the equivalence classes of certain pairs of R-actions and maps defined on the circle subject to five conditions. Consequently, we show that there are infinitely many smooth Sp(2, R)-actions on the space without fixed points up to equivariant diffeomorphisms.
We consider complete hyperbolic surfaces with punctures and holes. The aim of this paper is to show that there exisét pairs of hyperbolic surfaces of any genus not less than 56 which are iso-length-spectral but not isometric, for arbitrarily fixed numbers of punctures and holes.
We consider an algebraic D-module on a non-singular affine algebraic variety from an algorithmic viewpoint. Our main purpose is to show that the method of Grobner basis can be applied to concrete computation of invariants such as the characteristic variety of an algebraic D-module.
We study conformal vector fields on pseudo-Riemannian manifolds which are locally gradient fields. This is closely related with a certain differential equation for the Hessian of a real function. We obtain global solutions of the oscillator and peandulum equation for the Hessian of this function on a pseudo-Riemannian manifold, generalizing previous results by M. Obata, Y. Tashiro, and Y. Kerbrat. In particular, it turns out that the pendulum equation characterizes a certain conformal type of metrics carrying a conformal vector field with infinitely many zeros.