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020    3031368568 |q(paperback)
020    9783031368561 |q(paperback)
020     |z9783031368578 |qebook
024 7   |z10.1007/9783031368578 |2doi
035    (OCoLC)on1381292129
040    YDX |beng |erda |cYDX |dQGJ |dOHX |dUKMGB |dNHM |dOCLCO
050  4 QA613.619 |b.G55 2023
082 04 516.362 |223
100 1  Gil-Medrano, O. |q(Olga), |eauthor. |4aut
245 14 The volume of vector fields on Riemannian manifolds : |bmain results and open problems / |cOlga Gil-Medrano.
264  1 Cham, Switzerland : |bSpringer, |c[2023]
264  4  |c©2023
300    viii, 123 pages ; |c24 cm.
336    text |btxt |2rdacontent
337    unmediated |bn |2rdamedia
338    volume |bnc |2rdacarrier
490 1  Lecture notes in mathematics ; |v2336
504    Includes bibliographical references
520    "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to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results.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." -- |cProvided by publisher.
540    Current copyright fee: GBP19.00 |c42\0. |5Uk
650  0 Vector fields.
650  0 Riemannian manifolds.
650  6 Champs vectoriels.
650  6 Variétés de Riemann.
650  7 Vector fields |2fast
650  7 Riemannian manifolds |2fast
830  0 Lecture notes in mathematics (Springer-Verlag) ; |v2336.
902    940001858 |wcopy |120240123112115.0
914    (OCoLC)on1381292129 |bOCoLC |cmatch |d20240306 |eprocessed |f1381292129
956     |31850-9999 |uhttp://link.springer.com/ |xBLDSS