New connected sums with positive Ricci curvature

We construct a new infinite family of Ricci positive manifolds, generalising a well-known result of Sha and Yang.      

A New Proof of Calabi-Yau's Theorem

We give a new proof of Calabi-Yau's theorem on the volume growth of Rie- mannian manifolds with non-negative Ricci curvature.     

Riemannian curvature on the group of area-preserving diffeomorphisms (motions of fluid) of 2-sphere

Euler's equation for an incompressible fluid filled in a Riemannian manifold D is regarded as a geodesic equation on the group of volume-preserving diffeomorphisms of D provided with a one-sided invariant metric. A negative sectional curvature implies instability of the geodesic with respect to the corresponding flow and perturbation. The exponential growth of the perturbation is estimated from the values of the sectional curvatures.

This paper presents the expression of the components of Riemannian curvature tensor of the group of area-preserving diffeomorphisms of a 2-sphere in explicit formulas through 3 − j coefficients.     

Hyperfoliations on compact 3-manifolds with restrictions on the external curvature of leaves

C∞-foliations of codimension 1 on compact Riemannian 3-manifolds are studied. New classes of foliations, namely hyperbolic, elliptic, and parabolic foliations, are considered. Examples of such foliations are presented. In particular, aC∞-metric of nonnegative sectional curvature onS ³ such that the Reeb foliation is parabolic with respect to this metric is constructed. Analytic 3-manifolds with sectional curvature of constant sign admitting parabolic foliations are classified. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 651–659, May, 1998. The author wishes to express his thanks to Professor A. A. Borisenko for his supervision, and to Yu. A. Nikolaevskii for useful advice in the process of preparing the present paper.     

On the second order local comparison between perturbed maximum likelihood estimators and Rao's statistic as test statistics

A bias-adjusted maximum likelihood estimator (mle), which has been shown to possess certain optimality criteria as an estimate of θ (see Ghosh, J. K., Sinha, B. K., and Joshi, S. N. (1982). In Statistical Decision Theory and Related Topics III (S. S. Gupta and J. O. Berger, Eds.), Vol. 1, pp. 403–456. Academic Press, Orlando, FL) is compared with Rao's statistic as a test statistic for the standard two-sided testing problem. It is shown that Rao's statistic is locally superior to any bias-adjusted mle in the sense of Chandra and Joshi (1983, Sankhy Ser. A 45 226–246). A second interpretation of a conjecture of C. R. Rao is proposed and Rao's statistic is shown to be superior as a test statistic according to the new interpretation as well. The last fact provides an interesting supplement to the results of Chandra and Joshi (1983, Sankhy Ser. A 45 226–246). Furthermore, a partial reason for the inferiority of the likelihood ratio and Wald's statistic to Rao's statistic is supplied and certain regularity assumptions of the last paper are eliminated. Finally, the local powers of certain modified versions of Rao's and Wald's statistics (see Skovgaard, I. M. (1985). Ann. Statist. 13 534–551) are studied.     

Classifications of Isoparametric Hypersurfaces in Randers Space Forms

In this paper, we give the complete classifications of isoparametric hypersurfaces in Randers space forms. By studying the principal curvatures of anisotropic submanifolds in a Randers space (N, F) with the navigation data (h, W), we find that a Randers space form (N, F, dμ_BH) and the corresponding Riemannian space (N, h) have the same isoparametric hypersurfaces, but in general, their isoparametric functions are different. We give a necessary and sufficient condition for an isoparametric function of (N, h) to be isoparametric on (N, F, dμ_BH), from which we get some examples of isoparametric functions.     

Influence diagnostics for the proportional hazards model

Influence diagnostics based on Cook's curvature diagnostic (1986) are developed for the proportional hazards model. Three perturbation schemes are considered: perturbation of the likelihood, perturbation of the censoring information and perturbation of covariate values.     

爱因斯坦流形中超曲面的平均曲率流

本文证明了一个拼嵌的爱因斯坦流形中的任何超曲面在沿其平均曲率向量演化时，如果初发始曲面满足保持其截曲率为正的某些条件，则在有限时间内超曲而将收缩成一点。     

非线性再生散度模型基于统计曲率的诊断统计量

对非线性散度模型在Euclid空间建立几何结构。在此基础上，研究了均值漂移模型的曲率度量。从而导出相应Cook距离，似然距离等诊断统计量的二阶近似公式。     

SCALAR CURVATURES ON NONCOMPACT RIEMANN MANIFOLDS

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