|
Bitensor
In differential geometry and general relativity, a bitensor (or bi-tensor) is a tensorial object that depends on two points in a manifold, as opposed to ordinary tensors which depend on a single point. Bitensors provide a framework for describing relationships between different points in spacetime and are used in the study of various phenomena in curved spacetime. Definition A ''bitensor'' is a tensorial object that depends on two points in a manifold, rather than on a single point as ordinary tensors do. A ''bitensor field'' B can be formally defined as a map (mathematics), map from the Cartesian product, product manifold to an appropriate vector space B: M \times M \to V, where M is a smooth manifold and V is the vector space corresponding to the tensor space being considered. In the language of fiber bundles, a bitensor of type (r,s,r',s') is defined as a Section (fiber bundle), section of the exterior product, exterior tensor product bundle T^r_s M \boxtimes T^_ M, where T^r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Stanley Ruse
Harold Stanley Ruse (12 February 1905 – 20 October 1974) was an English mathematician, noteworthy for the development of the concept of locally harmonic spaces. He was Professor of Pure Mathematics at the University of Leeds. Early life and education Ruse was born in Hastings, England, Hastings, Sussex in 1905, the son of Frederick Ruse, a greengrocer and his wife, Lydia. He was educated at Hastings Grammar School and then studied Mathematics at Jesus College, Oxford, graduating with the degree of Bachelor of Arts, BA (Master of Arts (Oxford, Cambridge, and Dublin), later converted to MA). In 1927 he went to the University of Edinburgh as a Bruce of Grangehill research scholar. He was awarded the degree of Doctor of Science, DSc by Edinburgh five years later. Academic career Ruse remained at Edinburgh where he was appointed lecturer in mathematics in 1928. Additionally, he spent the academic year 1933–34 as a Rockefeller Research Fellow at Princeton University. He was to r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |