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- World Scientific Publishing Company 1995; US$ 99.00
By the Kobayashi-Hitchin correspondence, the authors of this book mean the isomorphy of the moduli spaces M st of stable holomorphic — resp. M HE of irreducible Hermitian–Einstein — structures in a differentiable complex vector bundle on a compact complex manifold. They give a complete proof of this result in the most general setting,... more...
- World Scientific Publishing Company 2000; US$ 105.00
The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler–Lagrangian equations.... more...
- World Scientific Publishing Company 1999; US$ 149.00
This text covers topics such as: contract metric R-harmonic manifolds; hypersurfaces in space forms with some constant curvature functions; manifolds of pseudodynamics; cubic forms generated by functions on projectively flat spaces; and distinguished submanifolds of a Sasakian manifold. more...
- World Scientific Publishing Company 1996; US$ 123.00
The object of this book is to introduce the reader to some of the most important techniques of modern global geometry. In writing it we had in mind the beginning graduate student willing to specialize in this very challenging field of mathematics. The necessary prerequisite is a good knowledge of the calculus with several variables, linear algebra... more...
- World Scientific Publishing Company 2001; US$ 95.00
These lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chih-Han Sah on various aspects of Hilbert's Third Problem: Are two Euclidean polyhedra with the same volume “scissors-congruent”, i.e. can they be... more...
- World Scientific Publishing Company 2001; US$ 163.00
This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition,... more...
- World Scientific Publishing Company 2001; US$ 274.00
Contents: Millennium Lecture — Cairo, 15 January 2000 (M Atiyah); Trends for Science and Mathematics in the 21st Century (P A Griffiths); Arabic Mathematics and Rewriting the History of Mathematics (R Rashed); The Paradigm Shift in Mathematics Education: A Scenario for Change (W Ebeid); Einstein's Theory of Spacetime and Gravity (J Ehlers);... more...
- World Scientific Publishing Company 2001; US$ 218.00
This book deals with the new class of one-dimensional variational problems — the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such... more...
- World Scientific Publishing Company 2001; US$ 127.00
In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P Finsler studied the variation problem in regular metric spaces. Around 1926, L Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important... more...
- World Scientific Publishing Company 2001; US$ 262.00
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... more...