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＜電子ブック＞
The Volume of Vector Fields on Riemannian Manifolds : Main Results and Open Problems / by Olga Gil-Medrano
(Lecture Notes in Mathematics. ISSN:16179692 ; 2336)

版	1st ed. 2023.
出版者	(Cham : Springer Nature Switzerland : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	VIII, 126 p : online resource
著者標目	*Gil-Medrano, Olga author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Mathematical analysis LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Geometry FREE:Analysis FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds
一般注記	This book focuses on the study of the volume of vector fields on Riemannian manifolds. Providing a thorough overview of research on vector fields defining minimal submanifolds, and on the existence and characterization of volume minimizers, it includes proofs of the most significant results obtained since the subject’s introduction in 1986. Aiming to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results. The presentation is direct and deviates substantially from the usual approaches found in the literature, requiring a significant revision of definitions, statements, and proofs. A wide range of topics is covered, including: a discussion on the conditions for a vector field on a Riemannian manifold to determine a minimal submanifold within its tangent bundle with the Sasaki metric; numerous examples of minimal vector fields (including those of constant length on punctured spheres); a thorough analysis of Hopf vector fields on odd-dimensional spheres and their quotients; and a description of volume-minimizing vector fields of constant length on spherical space forms of dimension three. Each chapter concludes with an up-to-date survey which offers supplementary information and provides valuable insights into the material, enhancing the reader's understanding of the subject. Requiring a solid understanding of the fundamental concepts of Riemannian geometry, the book will be useful for researchers and PhD students with an interest in geometric analysis HTTP:URL=https://doi.org/10.1007/978-3-031-36857-8

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