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Titlebook: Differential and Riemannian Manifolds; Serge Lang Textbook 1995Latest edition Springer-Verlag New York, Inc. 1995 De Rham cohomology.Hodge

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發(fā)表于 2025-3-21 19:11:25 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Differential and Riemannian Manifolds
編輯Serge Lang
視頻videohttp://file.papertrans.cn/279/278823/278823.mp4
叢書名稱Graduate Texts in Mathematics
圖書封面Titlebook: Differential and Riemannian Manifolds;  Serge Lang Textbook 1995Latest edition Springer-Verlag New York, Inc. 1995 De Rham cohomology.Hodge
描述This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes‘ theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one stud
出版日期Textbook 1995Latest edition
關(guān)鍵詞De Rham cohomology; Hodge decomposition; Riemannian geometry; cohomology; curvature; differential geometr
版次3
doihttps://doi.org/10.1007/978-1-4612-4182-9
isbn_softcover978-1-4612-8688-2
isbn_ebook978-1-4612-4182-9Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer-Verlag New York, Inc. 1995
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 22:46:50 | 只看該作者
Textbook 1995Latest editionf great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, cov
板凳
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地板
發(fā)表于 2025-3-22 05:42:00 | 只看該作者
Vector Bundles,es. In the chapters on differential forms and Riemannian metrics, we shall discuss in greater detail the constructions associated with multilinear alternating forms, and symmetric positive definite forms.
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An Easy Jump Start in Real-Time C++inking about the derivative of a map as a linear transformation. (In the finite dimensional case, when bases have been selected, the entries in the matrix of this transformation are the partial derivatives of the map.) We have repeated the proofs for the more important theorems, for the ease of the reader.
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發(fā)表于 2025-3-23 02:28:30 | 只看該作者
Garth Stahl,Erica Sharplin,Benjamin Kehrwaldes. In the chapters on differential forms and Riemannian metrics, we shall discuss in greater detail the constructions associated with multilinear alternating forms, and symmetric positive definite forms.
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發(fā)表于 2025-3-23 08:23:25 | 只看該作者
Inadequacies of existing control structurestem surrounding such forms. In order to have at least one application, we discuss the fundamental 2-form, and in the next chapter connect it with Riemannian metrics in order to construct canonically the spray associated with such a metric.
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