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 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 Selected Papers of Chuan Chih Hsiung written by Chuan-Chih Hsiung and published by World Scientific. This book was released on 2001 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains selected papers of Prof Chuan-Chih Hsiung, renowned mathematician in differential geometry and founder and editor-in-chief of a unique international journal in this field, the Journal of Differential Geometry . During the period of 1935OCo1943, Prof Hsiung was in China working on projective differential geometry under Prof Buchin Su. In 1946, he went to the United States, where he gradually shifted to global problems. Altogether Prof Hsiung has published about 100 research papers, from which he has selected 64 (in chronological order) for this volume. Contents: Projective Differential Geometry of a Pair of Plane Curves; A Projective Invariant of a Certain Pair of Surfaces; Affine Invariants of a Pair of Hypersurfaces; A Theorem on Surfaces with a Closed Boundary; Some Uniqueness Theorem on Riemannian Manifolds with Boundary; On the Group of Conformal Transformations of a Compact Riemannian Manifold; Minimal Immersions in Riemannian Spheres; A Remark on Pinched Manifolds with Boundary; Nonexistence of a Complex Structure on the Six-Sphere; Some Conditions for a Complex Structure; and other papers. Readership: Researchers in differential geometry."
Download or read book Selected Papers Of C C Hsiung written by Chuan-chih Hsiung and published by World Scientific. This book was released on 2001-04-30 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains selected papers of Prof Chuan-Chih Hsiung, renowned mathematician in differential geometry and founder and editor-in-chief of a unique international journal in this field, the Journal of Differential Geometry.During the period of 1935-1943, Prof Hsiung was in China working on projective differential geometry under Prof Buchin Su. In 1946, he went to the United States, where he gradually shifted to global problems. Altogether Prof Hsiung has published about 100 research papers, from which he has selected 64 (in chronological order) for this volume.
Download or read book Conformal Vector Fields Ricci Solitons and Related Topics written by Ramesh Sharma and published by Springer Nature. This book was released on 2024-01-19 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data. The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics.
Download or read book Riemannian Manifolds and Homogeneous Geodesics written by Valerii Berestovskii and published by Springer Nature. This book was released on 2020-11-05 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.
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 Dissertation Abstracts written by and published by . This book was released on 1962-04 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstracts of dissertations and monographs in microform.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1965 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transformation Groups in Differential Geometry written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Download or read book Index of Research Results written by United States. Air Force and published by . This book was released on 1962 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transactions of the American Mathematical Society written by and published by . This book was released on 1972 with total page 1040 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symmetries of Spacetimes and Riemannian Manifolds written by Krishan L. Duggal and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an upto date information on metric, connection and curva ture symmetries used in geometry and physics. More specifically, we present the characterizations and classifications of Riemannian and Lorentzian manifolds (in particular, the spacetimes of general relativity) admitting metric (i.e., Killing, ho mothetic and conformal), connection (i.e., affine conformal and projective) and curvature symmetries. Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of a comprehensive collection of the works of a very large number of researchers on all the above mentioned symmetries. (b) We have aimed at bringing together the researchers interested in differential geometry and the mathematical physics of general relativity by giving an invariant as well as the index form of the main formulas and results. (c) Attempt has been made to support several main mathematical results by citing physical example(s) as applied to general relativity. (d) Overall the presentation is self contained, fairly accessible and in some special cases supported by an extensive list of cited references. (e) The material covered should stimulate future research on symmetries. Chapters 1 and 2 contain most of the prerequisites for reading the rest of the book. We present the language of semi-Euclidean spaces, manifolds, their tensor calculus; geometry of null curves, non-degenerate and degenerate (light like) hypersurfaces. All this is described in invariant as well as the index form.
Download or read book U S Government Research Reports written by and published by . This book was released on 1964 with total page 2180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1965 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integral Formulas in Riemannian Geometry written by Kentarō Yano and published by Marcel Dekker. This book was released on 1970 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
