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Titlebook: Nonlinear Methods in Riemannian and K?hlerian Geometry; Delivered at the Ger Jürgen Jost Book 1991Latest edition Springer Basel AG 1991 cur

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書目名稱Nonlinear Methods in Riemannian and K?hlerian Geometry
副標(biāo)題Delivered at the Ger
編輯Jürgen Jost
視頻videohttp://file.papertrans.cn/668/667556/667556.mp4
圖書封面Titlebook: Nonlinear Methods in Riemannian and K?hlerian Geometry; Delivered at the Ger Jürgen Jost Book 1991Latest edition Springer Basel AG 1991 cur
描述In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent r?le in geometry. Let us Iist some of the most important ones: - harmonic maps between Riemannian and K?hlerian manifolds - minimal surfaces in Riemannian manifolds - Monge-Ampere equations on K?hler manifolds - Yang-Mills equations in vector bundles over m
出版日期Book 1991Latest edition
關(guān)鍵詞curvature; differential geometry; manifold; Minimal surface
版次2
doihttps://doi.org/10.1007/978-3-0348-7706-0
isbn_softcover978-3-0348-7708-4
isbn_ebook978-3-0348-7706-0
copyrightSpringer Basel AG 1991
The information of publication is updating

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Geometric Preliminaries,In this chapter, we assemble some basic material concerning connections on Riemannian, complex, and K?hler manifolds, and derive the nonlinear partial differential equations dealt with in this book, namely the harmonic map and Yang-Mills equations.
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Geometric applications of harmonic maps,In this section, we shall use our Bochner type formula (3.2.10),.for a harmonic .: . → . in order to derive some elementary results about the topology of nonpositively curved Riemannian manifolds. These results are well-known, and the present section therefore is included only for reasons of exposition.
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ntly, nonlinear PDE played a more and more pro~inent r?le in geometry. Let us Iist some of the most important ones: - harmonic maps between Riemannian and K?hlerian manifolds - minimal surfaces in Riemannian manifolds - Monge-Ampere equations on K?hler manifolds - Yang-Mills equations in vector bundles over m978-3-0348-7708-4978-3-0348-7706-0
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esearchers, travelers, military commanders, etc. who had relation to the Black Sea..It includes a multi-century chronology of the events that became the outstanding milestones in the history of development of the Black Sea – Azov Sea region. ?.978-3-662-51840-3978-3-642-55227-4Series ISSN 2626-1383 Series E-ISSN 2626-1405
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