Search

The objective of the current paper is essentially twofold. Firstly, to make clear the difference between two notions of rolling a Riemannian manifold over another, using a language accessible to a wider audience, in particular to readers with interest in applications. Secondly, we concentrate on rolling an important class of Riemannian manifolds. In the first part of the paper, the relation between intrinsic and extrinsic rollings is explained in detail, while in the second part we address rollings of symmetric spaces on flat spaces and complement the theoretical results with illustrative examples. [ABSTRACT FROM AUTHOR]

We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures. [ABSTRACT FROM AUTHOR]

In this paper we provide an analysis, both historical and mathematical, of two joint papers on the theory of connections by Élie Cartan and Jan Arnoldus Schouten that were published in 1926. These papers were the result of a fertile collaboration between the two eminent geometers that flourished in the two-year period 1925–1926. We describe the birth and the development of their scientific relationship especially in the light of unpublished sources that, on the one hand, offer valuable insight into their common research interests and, on the other hand, provide a vivid picture of Cartan's and Schouten's different technical choices. While the first part of this work is preeminently of a historical character, the second part offers a modern mathematical treatment of some contents of the two contributions. [ABSTRACT FROM AUTHOR]

We characterise sets of uniformly absolutely continuous norm in strongly symmetric spaces of τ-measurable operators. Applications are given to the study of relatively weakly compact and relatively compact sets and to compactness properties of operators dominated in the sense of complete positivity by compact or by Dunford-Pettis operators. [ABSTRACT FROM AUTHOR]