{"product_id":"9783642081491","title":"Natural Operations in Differential Geometry","description":"\u003ch1\u003eNatural Operations in Differential Geometry\u003c\/h1\u003e \u003ch2\u003eKolar, Ivan; Michor, Peter W.; Slovak, Jan\u003c\/h2\u003e \u003cp\u003eThe aim of this work is threefold: First it should be a monographical work on natural bundles and natural op­ erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2010-12-01\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783642081491\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-662-02950-3\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 434\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44398719238284,"sku":"9783642081491","price":116.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783642081491.jpg?v=1775766103","url":"https:\/\/lateknightbooks.com\/products\/9783642081491","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}