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Titlebook: Lie Sphere Geometry; With Applications to Thomas E. Cecil Book 2008Latest edition Springer-Verlag New York 2008 Dimension.Grad.curvature.di

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發(fā)表于 2025-3-21 16:48:23 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Lie Sphere Geometry
副標(biāo)題With Applications to
編輯Thomas E. Cecil
視頻videohttp://file.papertrans.cn/586/585714/585714.mp4
概述Provides the reader with all the necessary background to reach the frontiers of research in this area.Fills a gap in the literature; no other thorough examination of Lie sphere geometry and its applic
叢書名稱Universitext
圖書封面Titlebook: Lie Sphere Geometry; With Applications to Thomas E. Cecil Book 2008Latest edition Springer-Verlag New York 2008 Dimension.Grad.curvature.di
描述.This book provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean submanifold theory is established via the Legendre map, which provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres...This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry....Further key features of Lie Sphere Geometry 2/e:..- Provides the reader with all the necessary background to reach the frontiers of research in this area..- Fills a gap in the literature;
出版日期Book 2008Latest edition
關(guān)鍵詞Dimension; Grad; curvature; differential geometry; manifold; projective geometry
版次2
doihttps://doi.org/10.1007/978-0-387-74656-2
isbn_softcover978-0-387-74655-5
isbn_ebook978-0-387-74656-2Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag New York 2008
The information of publication is updating

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沙發(fā)
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0172-5939 r thorough examination of Lie sphere geometry and its applic.This book provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of
地板
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Lie Sphere Transformations,This is followed by a treatment of Laguerre geometry in Section 3.4. Finally, in Section 3.5, we show that the Lie sphere group is generated by the union of the groups of M?bius and Laguerre. There we also describe the place of Euclidean, spherical and hyperbolic metric geometries within the context of these more general geometries.
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https://doi.org/10.1007/978-0-387-74656-2Dimension; Grad; curvature; differential geometry; manifold; projective geometry
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發(fā)表于 2025-3-22 19:42:54 | 只看該作者
Thomas E. CecilProvides the reader with all the necessary background to reach the frontiers of research in this area.Fills a gap in the literature; no other thorough examination of Lie sphere geometry and its applic
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發(fā)表于 2025-3-22 22:51:19 | 只看該作者
Universitexthttp://image.papertrans.cn/l/image/585714.jpg
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Legendre Submanifolds,In this chapter, we develop the framework necessary to study submanifolds within the context of Lie sphere geometry.
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