Complete space-like submanifolds in locally symmetric semi-definite spaces

The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized     

Totally Real Submanifolds in a Quaternion Space Form

In this paper, we prove a theorem for n-dimensional totally real minimal submanifold immersed in quaternion space form.     

Immersions of Surfaces in Spinc-Manifolds with a Generic Positive Spinor

We define and discuss totally real and pseudoholomorphic immersions of real surfaces in a 4-manifold which, instead of an almost complex structure, carries only a framed spin^c-structure, that is, a spin^c-structure with a fixed generic section of its positive half-spinor bundle. In particular, we describe all pseudoholomorphic immersions of closed surfaces in the 4-sphere with a standard framed spin structure.     

Totally real minimal 2-spheres in quaternionic projective space

Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J, K} of complex structures on HPn satisfying U = -JI = K,JK = -KJ = /, KI = -IK = J. A surface M(？) HPn is called totally real, if at each point p ∈M the tangent plane TPM is perpendicular to I(TPM), J(TPM) and K(TPM). It is known that any surface M(？)RPn(？) HPn is totally real, where RPn (?) HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don't come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in Rp2m (？) RPn(？) HPn with 2m≤n. As a consequence we show that the Veronese sequences in KP2m (m≥1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space.     

Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements I

The first examples of totally geodesic Seifert surfaces are constructed for hyperbolic knots and links, including both free and totally knotted surfaces. Then it is proved that two bridge knot complements cannot contain totally geodesic orientable surfaces.     

A Question in the Theory of Totally Local Formations of Finite Groups

It is proved that all proper totally local subformations of a non one-generated totally local formation of finite groups are one-generated iff coincides with a formation of all soluble -groups, where ||=2.     

Doob–Meyer-Decomposition of Hilbert Space Valued Functions

(1) We give here a new proof of the Doob–Meyer-decomposition which is rather quick and elementary. It is more general in some aspects, and weaker in other aspects if compared to other approaches. The functions are defined on a totally ordered set with image in a Hilbert space. (2) We also give a second variant of the Doob–Meyer-decomposition; it is more specialized. (3) We apply (1) by reproving the Doléans-measure in a special setting and demonstrate that the stochastic integral could be defined on more general totally ordered time scales then .     

Totally knotted Seifert surfaces with accidental peripherals

We show that if there exists an essential accidental surface in the knot exterior, then a closed accidental surface also exists. As its corollary, we know boundary slopes of accidental essential surfaces are integral or meridional. It is shown that an accidental incompressible Seifert surface in knot exteriors in is totally knotted. Examples of satellite knots with arbitrarily high genus Seifert surfaces with accidental peripherals are given, and a Haken 3-manifold which contains a hyperbolic knot with an accidental incompressible Seifert surface of genus one is also given.

     

On the stability of the cyclic reduction without back substitution for tridiagonal systems

Componentwise error analysis for a modification of the cyclic reduction without back substitution for a tridiagonal system is presented. We consider relative roundoff errors and equivalent perturbations, so the main supposition is that all the data is nonzero. First, backward analysis for the computation of each component of the solution in separate is presented. Bounds on the relative equivalent perturbations are obtained depending on two constants. From these bounds it is easy to obtain a componentwise forward error analysis. Then the two constants are defined for some special classes of matrices, i.e. diagonally dominant (row or column), symmetric positive definite, totally nonnegative andM-matrices, and it is shown that the bounds for these classes of matrices are small.The author was supported by Grants MM-211/92 and MM-434/94 from the National Scientific Research Fund of the Bulgarian Ministry of Education and Science.     

Dirichlet Forms on Totally Disconnected Spaces and Bipartite Markov Chains

We use Dirichlet form methods to construct and analyze a general class of reversible Markov precesses with totally disconnected state space. We study in detail the special case of bipartite Markov chains. The latter processes have a state space consisting of an interior with a countable number of isolated points and a, typically uncountable, boundary. The equilibrium measure assigns all of its mass to the interior. When the chain is started at a state in the interior, it holds for an exponentially distributed amount of time and then jumps to the boundary. It then instantaneously re-enters the interior. There is a local time on the boundary. That is, the set of times the process is on the boundary is uncountable and coincides with the points of increase of a continuous additive functional. Certain processes with values in the space of trees and the space of vertices of a fixed tree provide natural examples of bipartite chains. Moreover, time-changing a bipartite chain by its local time on the boundary leads to interesting processes, including particular Lévy processes on local fields (for example, the p-adic numbers) that have been considered elsewhere in the literature.