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 Vector Fields on Manifolds with Boundary Discontinuities and Reversibility written by Marco Antonio Teixeira and published by . This book was released on 2001 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structural Stability of Vector Fields on 3 manifolds with Boundary written by M. J. Pacífico and published by . This book was released on 1983 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vector Fields and Infinitesimal Transformations on Riemannian Manifolds with Boundary written by Chuan-Chih Hsiung and published by . This book was released on 1943 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results of studies made of vector fields or infinitesimal transformations on compact Riemannian manifolds without boundary are extended to Riemannian manifolds with boundary. Fundamental formulas for Lie derivatives are given and the infinitesimal transformations and their generating vector fields are defined in terms of Lie derivatives. Necessary and sufficient conditions for a vector field on a manifold with zero tangential or normal component on a boundary to be a killing vector field are given. Conditions are obtained for the nonexistence of a nonzero conformal killing vector field on a manifold with zero tangential or normal component on the boundary, and necessary and sufficient conditions for a vector field on a manifold with zero tangential or normal component on the boundary to be a conformal killing vector field are obtained. It is shown that if the manifold has constant scalar curvature and admits a certain special infinitesimal nonhomothetic conformal motion leaving the boundary invariant, then the curvature is greater than zero. On a compact orientible Einstein manifold with the same boundary and curvature greater than zero, those special infinitesimal nonhomothetic conformal motions leaving the boundary invariant form a Lie algebra; a decomposition of this algebra with interrelations between its subalgebras is also obtained.
Download or read book Morse Theory Of Gradient Flows Concavity And Complexity On Manifolds With Boundary written by Katz Gabriel and published by World Scientific. This book was released on 2019-08-21 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it.The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters.
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 Manifolds Vector Fields and Differential Forms written by Gal Gross and published by Springer Nature. This book was released on 2023-04-25 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum. Questions sprinkled throughout the text engage students in active learning, and encourage classroom participation. Answers to these questions are provided at the end of the book, thus making it ideal for independent study. Material is further reinforced with homework problems ranging from straightforward to challenging. The book contains more material than can be covered in a single semester, and detailed suggestions for instructors are provided in the Preface.
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 Vector Fields and Infintesimal Transformations on Almost hermitian Manifolds with Boundary written by Arthur L. Hilt and published by . This book was released on 1963 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: An investigation is made of vector fields and infinitesimal transformations on almost-Hermitian manifolds with boundary. Riemannian manifolds are considered, as well as Lie derivatives over the manifolds, local boundary geodesic co-ordinates, and integral formulas. A Killing vector field on a compact orientable Riemannian manifold is discussed, and almost-Hermitian, almost-semiKahlerian, and almost-Kahlerian structures are defined. Contravariant analytic vector fields are given consideration on an almost-Hermitian manifold M(n) with boundary B(n-1), together with their relations to Killing, projective Killing, and conformal Killing vector fields. Covariant analytic vector fields on an almost-Hermitian manifold with boundary are studied as well as vector fields on an almost-Kahlerian manifold with boundary. (Author).
Download or read book Vector Fields and Infinitesimal Transformations on Almost Hermitian Manifolds with Boundary written by Arthur L. Hilt and published by . This book was released on 1961 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topology from the Differentiable Viewpoint written by John Willard Milnor and published by Princeton University Press. This book was released on 1997-12-14 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.
Download or read book Vector Fields on Singular Varieties written by Jean-Paul Brasselet and published by Springer Science & Business Media. This book was released on 2009-12-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.
Download or read book Morse smale Vector Fields on 4 manifolds with Boundary written by R. Labarca and published by . This book was released on 1986 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability of Morse Smale Vector Fields on Manifolds with Boundary written by Rafael Labarca and published by . This book was released on 1987 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds written by Gerd Grubb and published by American Mathematical Soc.. This book was released on 2005 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.
Download or read book Aspects of Boundary Problems in Analysis and Geometry written by Juan Gil and published by Springer Science & Business Media. This book was released on 2004-03-26 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.
Download or read book On the Boundary of the Set of Morse Smale Vector Fields on Two dimensional Manifolds written by Li Weigu and published by . This book was released on 1991 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
