Download or read book Vector Fields on Manifolds Phonotape written by and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Vector Fields on Manifolds written by Michael Francis Atiyah and published by Springer. This book was released on 2013-03-09 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle).

Download or read book The Volume of Vector Fields on Riemannian Manifolds written by Olga Gil-Medrano and published by Springer Nature. This book was released on 2023-07-31 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Vector fields on manifolds on manifolds written by Michael Francis Atiyah and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Vector Fields on Manifolds written by Lev S. Pontrjagin and published by . This book was released on 1949 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Vector Fields on Flag Manifolds microform written by Parameswaran Sankaran and published by National Library of Canada. This book was released on 1985 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Volume of Vector Fields on Riemannian Manifolds written by O. Gil-Medrano and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Vector Fields on Manifolds with Boundary written by Thomas Bruce Garner and published by . This book was released on 1971 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Holomorphic Vector Fields on Compact K hler Manifolds written by Yozō Matsushima and published by . This book was released on 1971 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Vector Fields on Manifolds written by Leon Karp and published by . This book was released on 1976 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Minimal Sets of Vector Fields on Manifolds written by June Margaret Marshall and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Vector Fields on Manifolds written by Phillip Gordon Schmitz and published by . This book was released on 2002 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Manifolds that Admit Parallel Vector Fields written by David James Welsh and published by . This book was released on 1982 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book America s Leading Manufacturers written by and published by . This book was released on 1921 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Waters of Coweeta written by United States. Forest Service and published by . This book was released on 1953 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication is designed to highlight the results of 20 years of streamflow studies at Coweeta, borrowing text and pictorial illustrations from the documentary film, "Waters of Coweeta."

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Download or read book Flying the Weather Map written by and published by . This book was released on 1945 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: