Submanifolds with curvature normals of constant length and the Gauss map

We show that a submanifold with curvature normal of constant length has constant principal curvatures under suitable global hypothesis. We construct local counterexamples to show that the global hypothesis can not be dropped

A geometric proof of the Karpelevich-Mostow's theorem

In this paper we give a geometric proof of the Karpelevich's theorem that asserts that a semisimple Lie subgroup of isometries, of a symmetric space of non compact type, has a totally geodesic orbit. In fact, this is equivalent to a well-known result of Mostow about existence of compatible Cartan decompositions

Corrigendum for "A geometric proof of the Karpelevich-Mostow theorem"

Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler proof of Karpelevich-Mostow theorem. We also include a short discussion of the original proof by Karpelevich

Holonomy and submanifold geometry

We survey applications of holonomic methods to the study of submanifold geometry, showing the consequences of some sort of extrinsic version of de Rham decomposition and Berger's Theorem, the so-called Normal Holonomy Theorem. At the same time, from geometric methods in submanifold theory we sketch very strong applications to the holonomy of Lorentzian manifolds. Moreover we give a conceptual modern proof of a result of Kostant for homogeneous space

A Practical Guide for Using Propensity Score Weighting in R

Propensity score weighting is one of the techniques used in controlling for selection biases in non-experimental studies. Propensity scores can be used as weights to account for selection assignment differences between treatment and comparison groups. One of the advantages of this approach is that all the individuals in the study can be used for the outcomes evaluation. In this paper, we demonstrate how to conduct propensity score weighting using R. The purpose is to provide a step-by-step guide to propensity score weighting implementation for practitioners. In addition to strengths, some limitations of propensity score weighting are discussed. Accessed 24,338 times on https://pareonline.net from June 27, 2015 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Propensity Scores: A Practical Introduction Using R

Background: This paper provides an introduction to propensity scores for evaluation practitioners.  Purpose: The purpose of this paper is to provide the reader with a conceptual and practical introduction to propensity scores, matching using propensity scores, and its implementation using statistical R program/software. Setting: Not applicable Intervention: Not applicable Research Design: Not applicable   Data Collection and Analysis: Not applicable Findings: In this demonstration paper, we describe the context in which propensity scores are used, including the conditions under which the use of propensity scores is recommended, as well as the basic assumptions needed for a correct implementation of the technique. Next, we describe some of the more common techniques used to conduct propensity score matching. We conclude with a description of the recommended steps associated with the implementation of propensity score matching using several packages developed in R, including syntax and brief interpretations of the output associated with every step. Keywords: propensity score analysis; propensity score matching; R

A Berger type normal holonomy theorem for complex submanifolds

We prove a kind of Berger-Simons' Theorem for the normal holonomy group of a complex submanifold of the projective spac