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The volume of vector fields on Riemannian manifoldsmain results and open problems /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The volume of vector fields on Riemannian manifoldsby Olga Gil-Medrano.
其他題名:	main results and open problems /
作者:	Gil-Medrano, O.
出版者:	Cham :Springer Nature Switzerland :2023.
面頁冊數:	viii, 126 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Vector fields.
電子資源:	https://doi.org/10.1007/978-3-031-36857-8
ISBN:	9783031368578$q(electronic bk.)

The volume of vector fields on Riemannian manifoldsmain results and open problems /
Gil-Medrano, O.

The volume of vector fields on Riemannian manifoldsmain results and open problems /[electronic resource] :by Olga Gil-Medrano. - Cham :Springer Nature Switzerland :2023. - viii, 126 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23361617-9692 ;. - Lecture notes in mathematics ;2035..

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to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results.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.

ISBN: 9783031368578$q(electronic bk.)

Standard No.: 10.1007/978-3-031-36857-8doiSubjects--Topical Terms:

384687
Vector fields.

LC Class. No.: QA613.619 / .G55 2023

Dewey Class. No.: 515.63

The volume of vector fields on Riemannian manifoldsmain results and open problems /
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