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The volume of vector fields on Riema...

Gil-Medrano, O.

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The volume of vector fields on Riemannian manifolds = main results and open problems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The volume of vector fields on Riemannian manifolds/ by Olga Gil-Medrano.
Reminder of title:	main results and open problems /
Author:	Gil-Medrano, O.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	viii, 126 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Vector fields. -
Online resource:	https://doi.org/10.1007/978-3-031-36857-8
ISBN:	9783031368578

The volume of vector fields on Riemannian manifolds = main 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 ;v. 2336..

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to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results.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

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

705428
Vector fields.

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

Dewey Class. No.: 515.63

The volume of vector fields on Riemannian manifolds = main results and open problems /
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300 $a viii, 126 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2336
520 $a 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.
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650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
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