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Author: IUrii Akhmetovich Aminov
Publisher:
ISBN:
Category : Geometry, Differential
Languages : en
Pages : 126
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Book Description
Author: IUrii Akhmetovich Aminov
Publisher:
ISBN:
Category : Geometry, Differential
Languages : en
Pages : 126
Get Book
Book Description
Author: I︠U︡riĭ Akhmetovich Aminov
Publisher:
ISBN: 9789667021146
Category : Geometry, Differential
Languages : en
Pages : 114
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Book Description
Author: Sadahiro Maeda
Publisher: World Scientific
ISBN: 9814566292
Category : Mathematics
Languages : en
Pages : 308
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Book Description
This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory. It also contains new results or brief surveys in these areas. This volume provides fundamental knowledge to readers (such as differential geometers) who are interested in the theory of real hypersurfaces in a non-flat complex space form. Contents:Homogeneous Submanifolds and Homogeneous Curves in Space Forms (S Maeda)Injectivity Property of Regular Curves and a Sphere Theorem (O Kobayashi)A Family of Complete Minimal Surfaces of Finite Total Curvature with Two Ends (S Fujimori and T Shoda)Minimal Surfaces in the Anti-De Sitter Spacetime (T Ichiyama and S Udagawa)Extrinsic Circular Trajectories on Geodesic Spheres in a Complex Projective Space (T Adachi)Geometry of Certain Lagrangian Submanifolds in Hermitian Symmetric Spaces (Y Ohnita)Some Real Hypersurfaces of Complex Projective Space (T Hamada)Contact Metric Hypersurfaces in Complex Space Forms (J T Cho and J Inoguchi)Non-Homogeneous η-Einstein Real Hypersurfaces in a 2-Dimensional Nonflat Complex Space Form (K Okumura)Sectional Curvatures of Ruled Real Hypersurfaces in a Nonflat Complex Space Form (H Tanabe and S Maeda)Totally Geodesic Köhler Immersions into a Complex Space Form, and a Non-Existence Theorem for Hessian Metrics of Positive Constant Hessian Sectional Curvature (T Noda and N Boumuki)Archimedean Theorems and W-Curves (D-S Kim and Y H Kim)On the Construction of Cohomogeneity One Special Lagrangian Submanifolds in the Cotangent Bundle of the Sphere (K Hashimoto)Self-Shrinkers of the Mean Curvature Flow (Q-M Cheng and Y Peng)Spectrum of Poly-Laplacian and Fractional Laplacian (L Zeng)Flat Centroaffine Surfaces with Non-Semisimple Tchebychev Operator (A Fujioka)The Total Absolute Curvature of Open Curves in EN (K Enomoto and J Itoh)Antipodal Sets of Compact Symmetric Spaces and the Intersection of Totally Geodesic Submanifolds (M S Tanaka)A Note on Symmetric Triad and Hermann Action (O Ikawa)Some Topics of Homogeneous Submanifolds in Complex Hyperbolic Spaces (T Hashinaga, A Kubo and H Tamaru)Austere Hypersurfaces in 5-Sphere and Real Hypersurfaces in Complex Projective Plane (J T Cho and M Kimura)On the Minimality of Normal Bundles in the Tangent Bundles Over the Complex Space Forms (T Kajigaya)Over-Determined Systems on Surfaces (N Ando) Readership: Researchers in differential geometry. Keywords:Minimal Surfaces;Morse Index;Real Hypersurfaces;Non-flat Complex Space Forms;Hopf Hypersurfaces;Symmetric Spaces;Homogeneous CurvesKey Features:Interesting papers on the theory of real hypersurfaces and the theory of minimal surfacesFeatures prominent contributors such as Y Ohnita, Q-M Cheng and O Kobayashi
Author: Bang-Yen Chen
Publisher: Courier Dover Publications
ISBN: 0486832783
Category : Mathematics
Languages : en
Pages : 193
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Book Description
The first two chapters of this frequently cited reference provide background material in Riemannian geometry and the theory of submanifolds. Subsequent chapters explore minimal submanifolds, submanifolds with parallel mean curvature vector, conformally flat manifolds, and umbilical manifolds. The final chapter discusses geometric inequalities of submanifolds, results in Morse theory and their applications, and total mean curvature of a submanifold. Suitable for graduate students and mathematicians in the area of classical and modern differential geometries, the treatment is largely self-contained. Problems sets conclude each chapter, and an extensive bibliography provides background for students wishing to conduct further research in this area. This new edition includes the author's corrections.
Author: Joel W. Robbin
Publisher: Springer Nature
ISBN: 3662643405
Category : Mathematics
Languages : en
Pages : 426
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Book Description
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Author: Chen Bang-yen
Publisher: World Scientific
ISBN: 9813208945
Category : Mathematics
Languages : en
Pages : 516
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Book Description
A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson–Walker models, are warped product manifolds. The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson–Walker's and Schwarzschild's. The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century. The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Author: Weihuan Chen
Publisher: World Scientific
ISBN: 9789810244767
Category : Mathematics
Languages : en
Pages : 368
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Book Description
http://www.worldscientific.com/worldscibooks/10.1142/4569
Author: Y. L. Xin
Publisher: World Scientific
ISBN: 9812386874
Category : Mathematics
Languages : en
Pages : 271
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Book Description
The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and author's own contributions to Bernstein type theorems for higher codimensions. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
Author: Maks Aĭzikovich Akivis
Publisher: North Holland
ISBN: 9780444897718
Category : Mathematics
Languages : en
Pages : 362
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Book Description
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations. Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.
Author: Franki Dillen
Publisher: World Scientific
ISBN: 9814549460
Category :
Languages : en
Pages : 334
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Book Description
This volume on pure and applied differential geometry, includes topics on submanifold theory, affine differential geometry and applications of geometry in engineering sciences. The conference was dedicated to the 70th birthday of Prof Katsumi Nomizu. Papers on the scientific work and life of Katsumi Nomizu are also included.
