2 edition of Minimal submanifolds in pseudo-Riemannian geometry found in the catalog.
Includes bibliographical references (p. 161-164) and index.
|LC Classifications||QA649 .A66 2011|
|The Physical Object|
|Pagination||xv, 167 p. :|
|Number of Pages||167|
Abstract: In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which includes the biharmonic equations for submanifolds of Riemannian manifolds as a special case. As applications, we proved that a pseudo-umbilical biharmonic pseudo-Riemannian submanifold of a pseudo-Riemannian manifold has constant Author: Yuxin Dong, Ye-Lin Ou. Book Review all pseudo-Riemannian submanifolds of the pseudo-Euclidean m-space, the hy-perbolic m-space and the de Sitter m-space, satisfying the condition that the mean curvature vector H is an eigenvector of the Laplacian. Some results on bihar-monic submanifolds, null 2-type submanifolds and spherical 2-type submanifolds are presented.
BIHARMONIC SUBMANIFOLDS IN NONFLAT LORENTZ 3-SPACE FORMS - Volume 85 Issue 3 - TORU SASAHARA Yuxin and Ou, Ye-Lin Biharmonic submanifolds of pseudo-Riemannian manifolds. Journal of Geometry and Physics, Vol. , p If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Cited by: However, most of the recent books on the subject still present the theory only in the Riemannian the first time, this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian geometry, only assuming from the reader some basic knowledge about manifold theory.
A number of recent results on pseudo-Riemannian submanifolds are also included. The second part of this book is on [symbol]-invariants, which was introduced in the early s by the author. The famous Nash embedding theorem published in was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds. the geometry of submanifolds Download the geometry of submanifolds or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get the geometry of submanifolds book now. This site is like a library, Use search box .
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On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemannian case. Request PDF | Minimal submanifolds in pseudo-Riemannian geometry | Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space Author: Henri Anciaux.
Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable This book provides an introduction to the subject in the general setting of pseudo-Riemannian geometry.
Minimal submanifolds in pseudo-Riemannian geometry. [Henri Anciaux] -- Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable.
We show that the only minimal submanifolds in this class are the totally geodesic n-spheres and Minimal submanifolds in pseudo-Riemannian geometry book one-parameter family of SO(n)-equivariant submanifolds which are described in terms of some Author: Henri Anciaux.
Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas.
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 : Bang-Yen Chen.
This book gives an extensive and in-depth overview of the theory of pseudo-Riemannian submanifolds and of the delta-invariants. It is written in an accessible and quite self-contained way. Hence it is recommendable for a very broad audience of students and mathematicians interested in the geometry of by: Minimal Submanifolds in Pseudo-Riemannian Geometry Since the foundational work of Lagrange on the differential equation to be satisfied by a Minimal surface of the Euclidean space, the theory of Minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis.
The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory.
A number of recent results on pseudo-Riemannian submanifolds are also second part of this book is on ë-invariants. Mathematics Subject Classiﬁcation.
58E20, 53C Key words and phrases. Biharmonic pseudo-Riemannian submanifolds, biharmonic hyper-surfaces, minimal submanifolds File Size: KB.
The theory of minimal submanifolds is one of the most beautiful and developed subjects of differential geometry. The aim of this chapter is to introduce a few of its general aspects.
This is a preview of subscription content, log in to check access. This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects.
System Upgrade on Tue, May 19th, at 2am (ET) During this period, E-commerce and registration of new users may not be available for up to 12 hours. Dear Colleagues, Submanifold theory can be thought of as a generalization of the study of surfaces in the 3-dimensional Euclidean space.
In the general theory, both the dimension of the submanifold and the codimension, which is the difference between the dimension of the ambient space and the dimension of the submanifold, can be arbitrarily high, and the ambient space does not need to be flat. The family of all the submanifolds of a given Riemannian or pseudo-Riemannian manifold is large enough to classify them into some interesting subfamilies such as minimal Author: J.L.
Cabrerizo, M. Fernández, J.S. Gómez. The Problem of Stability of Minimal Submanifolds in Riemannian and Pseudo-Riemannian Spaces Aminov, Yurij, HYPERSURFACES IN NON-FLAT PSEUDO-RIEMANNIAN SPACE FORMS SATISFYING A LINEAR CONDITION IN THE LINEARIZED OPERATOR OF A HIGHER ORDER MEAN CURVATURE Lucas, Pascual and Ramírez-Ospina, Héctor-Fabián, Taiwanese Journal of Mathematics Cited by: We then give a complete classification of biharmonic pseudo-Riemannian hypersurfaces of pseudo-Riemannian space forms with at most two distinct principal curvatures, and finally we use the classifications to give four methods to construct proper biharmonic pseudo-Riemannian submanifolds using precompositions of minimal by: 5.
Isotropic submanifolds Minimal Lagrangian Pseudo-Riemannian Isotropic Submanifolds - joint work with Luc Vrancken Universit e de Valenciennes et de Hainaut Cambr esis, Valenciennes, France November 20th, University of Granada, Spain Department of Geometry and Topology.
Minimal Submanifolds in Pseudo-Riemannian Geometry by Anciaux, Henri and a great selection of related books, art and collectibles available now at. The first two chapters of this frequently cited and newly updated 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 .Pseudo - Riemannian Geometry and Tensor Analysis by Rolf Sulanke Started February 1, surfaces in [EDG] it may be used as an interactive introductory textbook of diﬀer ential geometry.
Clearly, these notebooks don't cover the full content of an introductory course on this field. Section 4 is devoted to pseudo-Riemannian manifolds File Size: 45KB.The series will publish books of both theoretical and applied nature.
Theoretical volumes will focus among other topics on submanifold theory, Riemannian and pseudo-Riemannian geometry, minimal surfaces and submanifolds in Euclidean geometry.
Applications are found in biology, physics, engineering and other areas.