LEADER 05019nam 2200781Ia 450 001 9911019493603321 005 20200520144314.0 010 $a9786613273987 010 $a9781283273985 010 $a1283273985 010 $a9781118165461 010 $a1118165462 010 $a9781118165478 010 $a1118165470 035 $a(CKB)2550000000054247 035 $a(EBL)818923 035 $a(OCoLC)757394268 035 $a(SSID)ssj0000611693 035 $a(PQKBManifestationID)11362710 035 $a(PQKBTitleCode)TC0000611693 035 $a(PQKBWorkID)10666123 035 $a(PQKB)10011827 035 $a(SSID)ssj0000643644 035 $a(PQKBManifestationID)12227224 035 $a(PQKBTitleCode)TC0000643644 035 $a(PQKBWorkID)10675505 035 $a(PQKB)10500191 035 $a(MiAaPQ)EBC818923 035 $a(PPN)169733432 035 $a(Perlego)2757752 035 $a(EXLCZ)992550000000054247 100 $a19911017h19891969 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential geometry /$f[by] J. J. Stoker 210 $aNew York $cWiley-Interscience$d1989, c1969 215 $a1 online resource (428 p.) 225 1 $aPure and applied mathematics, v. 20 300 $a"Wiley classics edition published in 1989." 311 08$a9780471828259 311 08$a0471828254 311 08$a9780471504030 311 08$a0471504033 320 $aIncludes bibliographical references (p. 396-399) and index. 327 $aDifferential Geometry; CONTENTS; Chapter I Operations with Vectors; 1. The vector notation; 2. Addition of vectors; 3. Multiplication by scalars; 4. Representation of a vector by means of linearly independent vectors; 5. Scalar product; 6. Vector product; 7. Scalar triple product; 8. Invariance under orthogonal transformations; 9. Vector calculus; Chapter II Plane Curves; 1. Introduction; 2. Regular curves; 3. Change of parameters; 4. Invariance under changes of parameter; 5. Tangent lines and tangent vectors of a curve; 6. Orientation of a curve; 7. Length of a curve 327 $a1. Regular curves2. Length of a curve; 3. Curvature of space curves; 4. Principal normal and osculating plane; 5. Binormal vector; 6. Torsion ? of a space curve; 7. The Frenet equations for space curves; 8. Rigid body motions and the rotation vector; 9. The Darboux vector; 10. Formulas for ? and ?; 11. The sign of ?; 12. Canonical representation of a curve; 13. Existence and uniqueness of a space curve for given ? (S), ? (S); 14. What about ? = 0?; 15. Another way to define space curves; 16. Some special curves; Chapter IV The Basic Elements of Surface Theory 327 $a1. Regular surfaces in Euclidean space2. Change of parameters; 3. Curvilinear coordinate curves on a surface; 4. Tangent plane and normal vector; 5. Length of curves and first fundamental form; 6. Invariance of the first fundamental form; 7. Angle measurement on surfaces; 8. Area of a surface; 9. A few examples; 10. Second fundamental form of a surface; 11. Osculating paraboloid; 12. Curvature of curves on a surface; 13. Principal directions and principal curvatures; 14. Mean curvature H and Gaussian curvature K; 15. Another definition of the Gaussian curvature K; 16. Lines of curvature 327 $a17. Third fundamental form18. Characterization of the sphere as a locus of umbilical points; 19. Asymptotic lines; 20. Torsion of asymptotic lines; 21. Introduction of special parameter curves; 22. Asymptotic lines and lines of curvature as parameter curves; 23. Embedding a given arc in a system of parameter curves; 24. Analogues of polar coordinates on a surface; Chapter V Some Special Surfaces; 1. Surfaces of revolution; 2. Developable surfaces in the small made up of parabolic points; 3. Edge of regression of a developable; 4. Why the name developable? 327 $a5. Developable surfaces in the large1 330 $aThis classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis. 410 0$aPure and applied mathematics (Interscience Publishers) ;$vv. 20. 606 $aGeometry, Differential 606 $aManifolds (Mathematics) 615 0$aGeometry, Differential. 615 0$aManifolds (Mathematics) 676 $a516 676 $a516.7 700 $aStoker$b J. J$g(James Johnston),$f1905-$02708 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019493603321 996 $aDifferential geometry$91490790 997 $aUNINA