skip to content
Intrinsic geometry of convex surfaces Preview this item
ClosePreview this item

Intrinsic geometry of convex surfaces

Author: A D Aleksandrov; S S Kutateladze
Publisher: Boca Raton, FL : Chapman & Hall/CRC, 2006.
Edition/Format:   Print book : EnglishView all editions and formats

Published in English for the first time, this is the second part of a two volume set containing an extensive range of the most important papers by the geometer A.D. Alexandrov.


(not yet rated) 0 with reviews - Be the first.

More like this


Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...


Document Type: Book
All Authors / Contributors: A D Aleksandrov; S S Kutateladze
ISBN: 0415298024 9780415298025
OCLC Number: 55044661
Notes: Includes index.
Description: xiii, 426 pages : illustrations ; 25 cm.
Contents: BASIC CONCEPTS AND RESULTS The General Concept of Intrinsic Geometry and Its Problems Gaussian Intrinsic Geometry A Polyhedral Metric Development Passage from Polyhedra to Arbitrary Surfaces A Manifold with Intrinsic Metric Basic Concepts of Intrinsic Geometry Curvature Characteristic Properties of the Intrinsic Metric of a Convex Surface Some Special Features of Intrinsic Geometry Theorems of Intrinsic Geometry of Convex Surfaces General Propositions about the Intrinsic Metric General Theorems on Rectifiable Curves General Theorems on Shortest Arcs Nonoverlapping Condition for Shortest Arcs A Convex Neighborhood General Properties of Convex Domains Triangulation CHARACTERISTIC PROPERTIES OF THE INTRINSIC METRIC Convergence of Metrics of Convergent Convex Surfaces Convexity Condition for a Polyhedral Metric Convexity Condition for the Metric of a Convex Surface Consequences of the Convexity Condition ANGLE General Theorems on Addition of Angles Theorems on Addition of Angles on Convex Surfaces The Angle of a Sector Bounded by Shortest Arcs On Convergence of Angles The Tangent Cone The Spatial Meaning of the Angle Between Shortest Arcs CURVATURE Intrinsic Curvature Area of the Spherical Image Generalization of the Gauss Theorem Curvature of Borel Sets Set of Directions in Which It Is Impossible to Draw a Shortest Arc Curvature as a Measure of Non-Euclidicity of Space EXISTENCE OF A CONVEX POLYHEDRON WITH A GIVEN METRIC On Determination of a Metric from a Development The Idea of the Proof of the Realization Theorem Small Deformations of a Polyhedron Deformation of a Convex Polyhedral Angle Rigidity Theorem Realizability of the Metrics That Are Close to the Realized Metrics Smooth Passage from a Given Metric to a Realizable Metric Proof of the Realization Theorem EXISTENCE OF A CLOSED CONVEX SURFACE WITH A GIVEN METRIC The Result and the Method of Proof The Main Lemma on Convex Triangles Consequences of the Main Lemma on Convex Triangles The Complete Angle at a Point Curvature and Two Related Estimates Approximation of a Metric of Positive Curvature Realization of a Metric of Positive Curvature Given on the Sphere OTHER EXISTENCE THEOREMS Glueing Theorem Application of the Glueing Theorem to the Realization Theorems Realizability of a Complete Metric of Positive Curvature Manifolds on Which a Metric of Positive Curvature Can Be Given Uniqueness of a Convex Surface Various Definitions of a Metric of Positive Curvature CURVES ON CONVEX SURFACES The Direction of a Curve The Swerve of a Curve General Glueing Theorem Convex Domains Quasigeodesics A Circle AREA The Intrinsic Definition of Area The Extrinsic-Geometric Meaning of Area Extremal Properties of Pyramids and Cones THE ROLE OF SPECIFIC CURVATURE Intrinsic Geometry of a Surface Intrinsic Geometry of a Surface of Bounded Specific Curvature Shape of a Convex Surface in Dependence on Its Curvature GENERALIZATION Convex Surfaces in Spaces of Constant Curvature Realization Theorems in Spaces of Constant Curvature Surfaces of Indefinite Curvature BASICS OF CONVEX BODIES Convex Domains and Curves Convex Bodies. A Supporting Plane A Convex Cone Topological Types of Convex Bodies A Convex Polyhedron and the Convex Hull On Convergence of Convex Surfaces
Other Titles: Vnutrenni︠a︡i︠a︡ geometrii︠a︡ vypuklykh poverkhnosteĭ.
Responsibility: edited by S.S. Kutateladze ; translated from Russian by S. Vakhrameyev.
More information:


Editorial reviews

Publisher Synopsis

"This classic is quite readable and opens a deeper understanding of this field also through self-study without any special prerequisites ..." - H. Rindler, Wien, in Monatshefte fur Mathematik, Vol. Read more...

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...


Be the first.

Similar Items

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data

Primary Entity

<> # Intrinsic geometry of convex surfaces
    a schema:Book, schema:CreativeWork ;
   bgn:translationOfWork <> ; # Vnutrenni︠a︡i︠a︡ geometrii︠a︡ vypuklykh poverkhnosteĭ.
   library:oclcnum "55044661" ;
   library:placeOfPublication <> ; # Boca Raton, FL
   library:placeOfPublication <> ;
   schema:about <> ;
   schema:about <> ; # Convex surfaces
   schema:about <> ; # Geometry, Differential
   schema:bookFormat bgn:PrintBook ;
   schema:contributor <> ; # Semen Samsonovich Kutateladze
   schema:creator <> ; # Aleksandr Danilovich Aleksandrov
   schema:datePublished "2006" ;
   schema:exampleOfWork <> ; # Vnutrenni︠a︡i︠a︡ geometrii︠a︡ vypuklykh poverkhnosteĭ.
   schema:inLanguage "en" ;
   schema:isPartOf <> ; # Works.
   schema:isPartOf <> ; # A.D. Alexandrov, selected works ;
   schema:name "Intrinsic geometry of convex surfaces"@en ;
   schema:productID "55044661" ;
   schema:publication <> ;
   schema:publisher <> ; # Chapman & Hall/CRC
   schema:workExample <> ;
   wdrs:describedby <> ;

Related Entities

<> # Chapman & Hall/CRC
    a bgn:Agent ;
   schema:name "Chapman & Hall/CRC" ;

<> # Aleksandr Danilovich Aleksandrov
    a schema:Person ;
   schema:birthDate "1912" ;
   schema:deathDate "1999" ;
   schema:familyName "Aleksandrov" ;
   schema:givenName "Aleksandr Danilovich" ;
   schema:givenName "A. D." ;
   schema:name "Aleksandr Danilovich Aleksandrov" ;

<> # A.D. Alexandrov, selected works ;
    a bgn:PublicationSeries ;
   schema:hasPart <> ; # Intrinsic geometry of convex surfaces
   schema:name "A.D. Alexandrov, selected works ;" ;

<> # Convex surfaces
    a schema:Intangible ;
   schema:name "Convex surfaces"@en ;

<> # Geometry, Differential
    a schema:Intangible ;
   schema:name "Geometry, Differential"@en ;

<> # Semen Samsonovich Kutateladze
    a schema:Person ;
   schema:familyName "Kutateladze" ;
   schema:givenName "Semen Samsonovich" ;
   schema:givenName "S. S." ;
   schema:name "Semen Samsonovich Kutateladze" ;

<> # Aleksandr Danilovich Aleksandrov
    a schema:Person ;
   schema:birthDate "1912" ;
   schema:deathDate "1999" ;
   schema:familyName "Aleksandrov" ;
   schema:givenName "Aleksandr Danilovich" ;
   schema:givenName "A. D." ;
   schema:name "Aleksandr Danilovich Aleksandrov" ;

<> # Vnutrenni︠a︡i︠a︡ geometrii︠a︡ vypuklykh poverkhnosteĭ.
   schema:name "Vnutrenni︠a︡i︠a︡ geometrii︠a︡ vypuklykh poverkhnosteĭ." ;

    a schema:ProductModel ;
   schema:isbn "0415298024" ;
   schema:isbn "9780415298025" ;

<> # Vnutrenni︠a︡i︠a︡ geometrii︠a︡ vypuklykh poverkhnosteĭ.
    a schema:CreativeWork ;
   schema:inLanguage "ru" ;
   schema:name "Vnutrenni︠a︡i︠a︡ geometrii︠a︡ vypuklykh poverkhnosteĭ." ;

Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.