Projective differential geometry of submanifolds /
| Main Authors: | , |
|---|---|
| Corporate Author: | |
| Other Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam ; New York :
North-Holland,
1993
Amsterdam ; New York : 1993 |
| Series: | North-Holland mathematical library ;
49 North-Holland mathematical library ; v. 49 North-Holland mathematical library ; 49 North-Holland mathematical library ; v. 49 North-Holland mathematical library v. 49 |
| Subjects: |
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| 100 | 1 | |a Akivis, M. A |q (Maks Aĭzikovich) |1 http://viaf.org/viaf/24819758 | |
| 100 | 1 | |a Akivis, M. A |q (Maks Aĭzikovich) | |
| 100 | 1 | |a Akivis, M. A |q (Maks Aĭzikovich) |0 http://viaf.org/viaf/24819758 | |
| 100 | 1 | |a Akivis, M. A |q (Maks Aĭzikovich) | |
| 245 | 1 | 0 | |a Projective differential geometry of submanifolds / |c M.A. Akivis, V.V. Golʹdberg |
| 260 | |a Amsterdam ; |a New York : |b North-Holland, |c 1993 | ||
| 263 | |a 9305 | ||
| 264 | 1 | |a Amsterdam ; |a New York : |b North-Holland, |c 1993 | |
| 300 | |a 362 p | ||
| 300 | |a xi, 362 p. : |b ill. ; |c 23 cm | ||
| 300 | |a xi, 362 p. : |b ill. ; |c 24 cm | ||
| 300 | |a xi, 362 p. ; |c 23 cm | ||
| 300 | |a xi, 362 pages : |b illustrations ; |c 23 cm | ||
| 300 | |a xi, 362 pages ; |c 23 cm | ||
| 336 | |a text |2 rdacontent | ||
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| 440 | 0 | |a North-Holland mathematical library ; |v 49 | |
| 440 | 0 | |a North-Holland mathematical library ; |v v. 49 | |
| 490 | 1 | |a North-Holland mathematical library ; |v 49 | |
| 490 | 1 | |a North-Holland mathematical library ; |v v. 49 | |
| 490 | 1 | |a North-Holland mathematical library |v 49 | |
| 500 | |a This WorldCat-derived record is shareable under Open Data Commons ODC-BY, with attribution to OCLC |5 CTY | ||
| 504 | |a Includes bibliographical references (p. 297-331) and index | ||
| 504 | |a Includes bibliographical references (p. 297-331) and indexes | ||
| 504 | |a Includes bibliographical references (p. 297-334) and index | ||
| 504 | |a Includes bibliographical references (pages 297-331) and index | ||
| 504 | |a Includes bibliographical references and index | ||
| 504 | |a Includes bibliographical references | ||
| 505 | 2 | |a 3.5. The Laplace Transforms of Conjugate Nets and Their Generalizations -- 3.6. Conic m-Conjugate Systems -- Ch. 4. Tangentially Degenerate Submanifolds -- 4.1. Basic Notions and Equations -- 4.2. Focal Images -- 4.3. Decomposition of Focal Images -- 4.4. The Holonomicity of the Focal Net -- 4.5. Some Other Classes of Tangentially Degenerate Submanifolds -- 4.6. Manifolds of Hypercones -- 4.7. Parabolic Submanifolds without Singularities in Euclidean and Non-Euclidean Spaces -- Ch. 5. Submanifolds with Asymptotic and Conjugate Distributions -- 5.1. Distributions on Submanifolds of a Projective Space -- 5.2. Asymptotic Distributions on Submanifolds -- 5.3. Submanifolds with a Complete System of Asymptotic Distributions -- 5.4. Three-Dimensional Submanifolds Carrying a Net of Asymptotic Lines -- 5.5. Submanifolds with a Complete System of Conjugate Distributions -- Ch. 6. Normalized Submanifolds in a Projective Space --^ | |
| 505 | 2 | |a 6.1. The Problem of Normalization of a Submanifold in a Projective Space -- 6.2. The Affine Connection on a Normalized Submanifold -- 6.3. The Connection in the Normal Bundle -- 6.4. Submanifolds with a Flat Normal Connection -- 6.5. Intrinsic Normalization of Submanifolds -- 6.6. Normalization of Submanifolds Carrying a Conjugate Net of Lines -- Ch. 7. Projective Differential Geometry of Hypersurfaces -- 7.1. Basic Equations of the Theory of Hypersurfaces -- 7.2. Osculating Hyperquadrics of a Hypersurface -- 7.3. Invariant Normalizations of a Hypersurface -- 7.4. The Rigidity Problem in a Projective Space -- 7.5. The Geometry of a Surface in Three-Dimensional Projective Space -- 7.6. The Geometry of Hyperbands -- Ch. 8. Algebraization Problems in Projective Differential Geometry -- 8.1. The First Generalization of Reiss' Theorem -- 8.2. The Second Generalization of Reiss' Theorem -- 8.3. Degenerate Monge's Varieties -- 8.4. Submanifolds with Degenerate Bisecant Varieties | |
| 505 | 2 | |a Ch. 1. Preliminaries -- 1.1. Vector Spaces -- 1.2. Differentiable Manifolds -- 1.3. Projective Space -- 1.4. Some Algebraic Manifolds -- Ch. 2. The Foundations of Projective Differential Geometry of Submanifolds -- 2.1. Submanifolds in a Projective Space and Their Tangent Subspaces -- 2.2. The Second Fundamental Form of a Submanifold -- 2.3. Osculating Subspaces and Fundamental Forms of Higher Orders of a Submanifold -- 2.4. Asymptotic and Conjugate Directions of Different Orders on a Submanifold -- 2.5. Some Particular Cases and Examples -- 2.6. Classification of Points of Submanifolds by Means of the Second Fundamental Form -- Ch. 3. Submanifolds Carrying a Net of Conjugate Lines -- 3.1. Basic Equations and General Properties -- 3.2. The Holonomicity of the Conjugate Net [actual symbol not reproducible] -- 3.3. Classification of Conjugate Nets [actual symbol not reproducible] -- 3.4. Some Existence Theorems --^ | |
| 505 | 2 | 0 | |g Ch. 1 |t Preliminaries. |g 1.1. |t Vector Spaces. |g 1.2. |t Differentiable Manifolds. |g 1.3. |t Projective Space. |g 1.4. |t Some Algebraic Manifolds -- |g Ch. 2. |t The Foundations of Projective Differential Geometry of Submanifolds. |g 2.1. |t Submanifolds in a Projective Space and Their Tangent Subspaces. |g 2.2. |t The Second Fundamental Form of a Submanifold. |g 2.3. |t Osculating Subspaces and Fundamental Forms of Higher Orders of a Submanifold. |g 2.4. |t Asymptotic and Conjugate Directions of Different Orders on a Submanifold. |g 2.5. |t Some Particular Cases and Examples. |g 2.6. |t Classification of Points of Submanifolds by Means of the Second Fundamental Form -- |g Ch. 3. |t Submanifolds Carrying a Net of Conjugate Lines. |g 3.1. |t Basic Equations and General Properties. |g 3.2. |t The Holonomicity of the Conjugate Net [actual symbol not reproducible]. |g 3.3. |t Classification of Conjugate Nets [actual symbol not reproducible]. |g 3.4. |t Some Existence Theorems. |g 3.5. |t The Laplace Transforms of Conjugate Nets and Their Generalizations. |g 3.6. |t Conic m-Conjugate Systems -- |g Ch. 4. |t Tangentially Degenerate Submanifolds. |g 4.1. |t Basic Notions and Equations. |g 4.2. |t Focal Images. |g 4.3. |t Decomposition of Focal Images. |g 4.4. |t The Holonomicity of the Focal Net. |g 4.5. |t Some Other Classes of Tangentially Degenerate Submanifolds. |g 4.6. |t Manifolds of Hypercones. |g 4.7. |t Parabolic Submanifolds without Singularities in Euclidean and Non-Euclidean Spaces -- |g Ch. 5. |t Submanifolds with Asymptotic and Conjugate Distributions. |g 5.1. |t Distributions on Submanifolds of a Projective Space. |g 5.2. |t Asymptotic Distributions on Submanifolds. |g 5.3. |t Submanifolds with a Complete System of Asymptotic Distributions. |g 5.4. |t Three-Dimensional Submanifolds Carrying a Net of Asymptotic Lines. |g 5.5. |t Submanifolds with a Complete System of Conjugate Distributions -- |g Ch. 6. |t Normalized Submanifolds in a Projective Space. |g 6.1. |t The Problem of Normalization of a Submanifold in a Projective Space. |g 6.2. |t The Affine Connection on a Normalized Submanifold. |g 6.3. |t The Connection in the Normal Bundle. |g 6.4. |t Submanifolds with a Flat Normal Connection. |g 6.5. |t Intrinsic Normalization of Submanifolds. |g 6.6. |t Normalization of Submanifolds Carrying a Conjugate Net of Lines -- |g Ch. 7. |t Projective Differential Geometry of Hypersurfaces. |g 7.1. |t Basic Equations of the Theory of Hypersurfaces. |g 7.2. |t Osculating Hyperquadrics of a Hypersurface. |g 7.3. |t Invariant Normalizations of a Hypersurface. |g 7.4. |t The Rigidity Problem in a Projective Space. |g 7.5. |t The Geometry of a Surface in Three-Dimensional Projective Space. |g 7.6. |t The Geometry of Hyperbands -- |g Ch. 8. |t Algebraization Problems in Projective Differential Geometry. |g 8.1. |t The First Generalization of Reiss' Theorem. |g 8.2. |t The Second Generalization of Reiss' Theorem. |g 8.3. |t Degenerate Monge's Varieties. |g 8.4. |t Submanifolds with Degenerate Bisecant Varieties. |
| 590 | |a Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund | ||
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