Journal•ISSN: 0003-889X
Archiv der Mathematik
Springer Science+Business Media
About: Archiv der Mathematik is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Abelian group & Group (mathematics). It has an ISSN identifier of 0003-889X. Over the lifetime, 9035 publications have been published receiving 81420 citations. The journal is also known as: Archives mathématiques & AdM.
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614 citations
TL;DR: In this paper, the authors define an immersion from an n-dimensional (n > 0) mani- fold into a Euclidean re, space and define the Laplacian operator of M with respect to the induced metric.
Abstract: By BANG-YEN CHEN 1. Introduction. Let x: M -* E" be an immersion from an n-dimensional (n > 0) mani- fold into a Euclidean re, space. Denote by A the Laplacian operator of M with respect to the induced metric. Then we have the following formula of Beltrami: (1.1)
381 citations
367 citations
353 citations
TL;DR: In this article, it was shown that there is a 1-1 correspondence between commutative monads and symmetric monoidal monads, and the main computational work needed to construct an equivalence between possible strengths 8tA,B: A c+A c+B+A T +A T ~ B T
Abstract: In [4] we proved that a commutative monad on a symmetric monoidal closed category carries the structure of a symmetric monoidal monad ([4], Theorem 32) We here prove the converse, so that, taken together, we have: there is a 1-1 correspondence between commutative monads and symmetric monoidal monads (Theorem 23 below) The main computational work needed consists in constructing an equivalence between possible strengths 8tA,B: A c~ B -+ A T ~ B T
289 citations