Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors.
In recent years, research in K3 surfaces and Calabi-Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics-in particular, in string theory.
Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques.
Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems.
This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems.
The papers in this volume are an outgrowth of the lectures and informal discussions that took place during the workshop on "e;The Geometry of Hamiltonian Systems"e; which was held at MSRl from June 5 to 16, 1989.
This volume derives from a workshop on differential geometry, calculus of vari- ations, and computer graphics at the Mathematical Sciences Research Institute in Berkeley, May 23-25, 1988.
This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics.
"e;Spherical soap bubbles"e;, isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry.
In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges.
This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition.
A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum.
During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions.
The aim of this book is to provide a short but complete exposition of the logical structure of classical relativistic electrodynamics written in the language and spirit of coordinate-free differential geometry.
This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995.
This monograph is based on the author's results on the Riemannian ge- ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature.
The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po- sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans- lation invariant part of its total angular (four) momentum M.
This book is an outgrowth of the Workshop on "e;Regulators in Analysis, Geom- etry and Number Theory"e; held at the Edmund Landau Center for Research in Mathematical Analysis of The Hebrew University of Jerusalem in 1996.
Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education.
Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups.
This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology).
