作者：LuisSantalo[著]
页数：404
出版社：世界图书出版公司
出版日期：2009
ISBN：9787510004933
电子书格式：pdf/epub/txt
内容简介
Though its title “Integral Geometry” may appear somewhat unusual in thiscontext it is nevertheless quite appropriate, for Integral Geometry is anoutgrowth of what in the olden days was referred to as “geometric probabil-ities.”
Originating, as legend has it, with the Buffon needle problem （which afternearly two centuries has lost little of its elegance and appeal）, geometricprobabilities have run into difficulties culminating in the paradoxes ofBertrand which threatened the fledgling field with banishment from the homeof Mathematics. In rescuing it from this fate, Poincar6 made the suggestionthat the arbitrariness of definition underlying the paradoxes could be removedby tying closer the definition of probability with a geometric group of which itwould have to be an invariant.
本书特色
Now available in the Cambridge Mathematical Library, the classic work from Luis Santalo. Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments, however, have proved useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). The book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used to complement courses on differential geometry, Lie groups or probability, or differential geometry. It is ideal both as a reference and for those wishing to enter the field.
目录
Foreword
Preface
Part Ⅰ.INTEGRAL GEOMETRY IN THE PLANE
Chapter 1.Convex Sets in the Plane
Chapter 2.Sets of Points and Poisson Processes in the Plane
Chapter 3.Sets of Lines in the Plane
Chatper 4.Pairs of Points and Pairs of Lines
Chapter 5.Sets of Strips in the Plane
Chapter 6.The Group of Motions in the Plane:Kinematic Density
Chapter 7.Fundamental Formulas of Poincare and Blaschke
Chapter 8.Lattices of Figures
Part Ⅱ.GENERAL INTEGRAL GEOMETRY
Chapter 9.Differential Forms and Lie Groups
Chapter 10.Density and Measure in Homogeneous Spaces
Chapter 11.The Affine Groups
Chpater 12.The Group of Motions in En
Part Ⅲ.INTEGRAL GEOMETRY IN En
Chapter 13.Convex Sets in En
Chapter 14.Linear Subspaces,Convex Sets,and Compact Manifolds
Chapter 15.The Kinematic Density in En
Chpater 16.Geometric and Statistical Applications; Stereology
Part Ⅳ.INTEGRAL GEOMETRY IN SPACES OF CONSTANT CURVATURE
Chapter 17.Noneuclidean Integral Geometry
Chapter 18.Crofton’s Formulas and the Kinematic FundaⅠmental Formula in Noneuclidean Spaces
Chapter 19.Integral Geometry and Foliated Spaces; Trends in Integral Geometry
Appendix.Differential Forms and Exterior Calculus
Bibliography and References
Author Index
Subject Index
