A manifold is a topological space that locally resembles Euclidean space near each point, so that a manifold's global structure can be complicated even though every small neighbourhood around any point looks like ordinary flat space. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Source Manifold (Wikipedia)
Tensor, Concepts Tensor fields defined at each point of a manifold, varying smoothly across it, are the standard way tensors extend beyond a single vector space into differential geometry.
Additional Source Tensor (Wikipedia)Lead section
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Source Manifold (Wikipedia)
Source Manifold (Wikipedia)
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1. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsRiemann biography, 1854 habilitation lectureQuote, Riemann biography, 1854 habilitation lecture
Riemann's lecture Ueber die Hypothesen welche der Geometrie zu Grunde liegen, delivered on 10 June 1854, became a classic of mathematics.
Manifold (Wikipedia)
Wikimedia Foundationlead paragraph
a manifold is a topological space that locally resembles Euclidean space near each point
Associated With: Bernhard Riemann, history section
Riemann was the first one to do extensive work generalizing the idea of a surface to higher dimensions.
View the Source Tensor (Wikipedia)
Wikimedia FoundationAssociated With: Tensor, Lead sectionQuote, Associated With: Tensor, Lead section
a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space
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