Volume of Vector Fields on Riemannian Manifolds

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.

“The monograph under review provides a quite complete survey of up-to-date results on the minimality of vector fields on odd-dimensional spheres and more general Riemannian manifolds. Besides, it can be recommended as a self-consistent textbook introducing the reader to modern techniques for studying the extrinsic geometry of vector fields. the monograph includes a lot of intriguing open questions and conjectures which may serve as a novel source of inspiration for further researches … .” (Vasyl Gorkaviy, zbMATH 1536.53003, 2024)

• - 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.