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We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51717949325585,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51717949653265,"sku":"NGR9783031012792","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3031012798.jpg?v=1786615532"},{"product_id":"geometry-of-walker-manifolds-book-peter-gilkey-9783031012693","title":"The Geometry of Walker Manifolds","description":"Basic Algebraic Notions.- Basic Geometrical Notions.- Walker Structures.- Three-Dimensional Lorentzian Walker Manifolds.- Four-Dimensional Walker Manifolds.- The Spectral Geometry of the Curvature Tensor.- Hermitian Geometry.- Special Walker Manifolds.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":52152826036497,"sku":"NGR9783031012693","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52431919153425,"sku":"NLS9783031012693","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031012693.jpg?v=1757617994"},{"product_id":"applications-of-affine-and-weyl-geometry-book-peter-gilkey-9783031012778","title":"Applications of Affine and Weyl Geometry","description":"Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. The fourth chapter deals with Kahler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kahler geometry.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":52152892948753,"sku":"NGR9783031012778","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52431980953873,"sku":"NLS9783031012778","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031012778.jpg?v=1757618213"},{"product_id":"aspects-of-differential-geometry-ii-book-peter-gilkey-9783031012808","title":"Aspects of Differential Geometry II","description":"Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book I deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kahler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincare duality, and the Kunneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book I concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":52152909529361,"sku":"NGR9783031012808","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52431063712017,"sku":"NLS9783031012808","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031012808.jpg?v=1785947698"},{"product_id":"aspects-of-differential-geometry-v-book-esteban-calviolouzao-9783031013041","title":"Aspects of Differential Geometry V","description":"Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52431634071825,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52431634661649,"sku":"NLS9783031013041","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031013041.jpg?v=1759173077"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-peter-gilkey.oembed","provider":"World of Books ","version":"1.0","type":"link"}