Olga Gil-Medrano
The Volume of Vector Fields on Riemannian Manifolds: Main Results and Open Problems
The Volume of Vector Fields on Riemannian Manifolds: Main Results and Open Problems
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- More about The Volume of Vector Fields on Riemannian Manifolds: Main Results and Open Problems
The book explores vector fields on Riemannian manifolds, focusing on minimal submanifolds and volume minimizers, with proofs of significant results since 1986. It covers various topics, including minimal vector fields, Hopf vector fields, and volume-minimizing vector fields on spherical space forms. It requires a strong foundation in Riemannian geometry and is suitable for researchers and PhD students in geometric analysis.
Format: Paperback / softback
Length: 126 pages
Publication date: 01 August 2023
Publisher: Springer International Publishing AG
The book delves into the study of vector fields on Riemannian manifolds, encompassing the exploration of minimal submanifolds and the investigation of volume minimizers. It presents a comprehensive overview of research on these topics, including proofs of significant results since their introduction in 1986. With the aim of inspiring further research, it highlights intriguing open problems and showcases previously unpublished results. The presentation deviates significantly from traditional approaches, necessitating a substantial revision of definitions, statements, and proofs. The book covers a wide range of topics, including the conditions for a vector field to determine a minimal submanifold within its tangent bundle with the Sasaki metric, numerous examples of minimal vector fields, 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 that provides supplementary information and valuable insights into the material, enhancing the reader's understanding of the subject. The book requires a solid understanding of the fundamental concepts of Riemannian geometry and is suitable for researchers and PhD students with an interest in geometric analysis.
Dimension: 235 x 155 (mm)
ISBN-13: 9783031368561
Edition number: 1st ed. 2023
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