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gil-medrano olga - the volume of vector fields on riemannian manifolds

The Volume of Vector Fields on Riemannian Manifolds Main Results and Open Problems

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Lingua: Inglese


Pubblicazione: 08/2023
Edizione: 1st ed. 2023


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to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results.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


- 1. Introduction. - 2. Minimal Sections of Tensor Bundles. - 3. Minimal Vector Fields of Constant Length on the Odd-Dimensional Spheres. - 4. Vector Fields of Constant Length of Minimum Volume on the Odd-Dimensional Spherical Space Forms. - 5. Vector Fields of Constant Length on Punctured Spheres.


Olga Gil-Medrano (1956, Spain) is a retired Full Professor at the University of Valencia, Spain. A leading specialist in the study of vector field volumes on Riemannian manifolds, her research also includes other topics of geometric analysis, such as the geometrical theory of foliations, the Yamabe problem, the geometry of spaces of metrics and other sections of tensor bundles, and variational problems on these spaces.  She received the Medal of the Royal Spanish Mathematical Society (RSME) in 2021.

Altre Informazioni



Condizione: Nuovo
Collana: Lecture Notes in Mathematics
Dimensioni: 235 x 155 mm Ø 221 gr
Formato: Brossura
Illustration Notes:VIII, 126 p.
Pagine Arabe: 126
Pagine Romane: viii

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