3-Quasi-Sasakian manifolds

In the present article we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular, we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the vertical distribution is a minimum of the corrected energy.      

Pseudo-conformal quaternionic CR structure on (4n + 3)-dimensional manifolds

We study an integrable, nondegenerate codimension 3-subbundle ${\mathcal{D}}We study an integrable, nondegenerate codimension 3-subbundle on a (4n + 3)-manifold M whose fiber supports the structure of 4n-dimensional quaternionic vector space. It is thought of as a generalization of quaternionic CR structure. We single out an -valued 1-form ω locally on a neighborhood U such that and construct the curvature invariant on (M, ω) whose vanishing gives a uniformization to flat quaternionic CR geometry. The invariant obtained on M has the same formula as that of pseudo-quaternionic K?hler 4n-manifolds. From this viewpoint, we exhibit a quaternionic analogue of Chern-Moser’s CR structure. The authors are grateful to ESI for financial support and hospitality during the preparation of this work. The first author acknowledge the support by Grant FWF Project P17108-N04 (Vienna) and Grant N MSM 0021622409 of the Ministry of Education, Youth and Sports (Brno).     

Riemannian Submersions and Riemannian Manifolds with Einstein--Weyl Structures

The main results of this paper are as follows. (a) Let : M N be a non-trivial Riemannian submersion with totally geodesic fibers of dimension 1 over an Einstein manifold N. If M is compact and admits a standard Einstein--Weyl structure with constant Einstein--Weyl function, then N admits a Kähler structure andM a Sasakian structure. (b) Let be a Riemannian submersion with totally geodesic fibers and N an Einstein manifold of positive scalar curvature . If M admits a standard Sasakian structure, then M admits an Einstein--Weyl structure with constant Einstein--Weyl function.     

G3连续过渡曲面的构造

过渡曲面在CAD／CAM中具有十分重要的作用,其构造与风荷连续性,几何不变量密切相关。本文通过对几何不变量法曲率,测地挠率和几何连续关系的推导,得到构造G^3几何连续过渡曲面的充分条件,结合连接线定理,用超限插值法解决了两个参数面间G3几何连续时渡问题。     

Reduction of the Gibbs phenomenon for smooth functions with jumps by the -algorithm

Recently, Brezinski has proposed to use Wynn's ε-algorithm in order to reduce the Gibbs phenomenon for partial Fourier sums of smooth functions with jumps, by displaying very convincing numerical experiments. In the present paper we derive analytic estimates for the error corresponding to a particular class of hypergeometric functions, and obtain the rate of column convergence for such functions, possibly perturbed by another sufficiently differentiable function. We also analyze the connection to Padé–Fourier and Padé–Chebyshev approximants, including those recently studied by Kaber and Maday.