| Introduction | p. 1 |
| Preliminaries | p. 7 |
| Real Spaces with Bilinear Metric | p. 7 |
| Moving Frames | p. 8 |
| (Pseudo-)Riemannian Manifolds | p. 10 |
| Standard Models of Space and Spacetime Forms | p. 11 |
| Symmetric (Pseudo-)Riemannian Manifolds | p. 13 |
| Semisymmetric (Pseudo-)Riemannian Manifolds | p. 16 |
| Submanifolds in Space Forms | p. 23 |
| A Submanifold and Its Adapted Frame Bundle | p. 23 |
| Higher-Order Fundamental Forms | p. 26 |
| Fundamental Identities | p. 29 |
| Osculating and Normal Subspaces of Higher Order | p. 29 |
| Parallel Submanifolds | p. 33 |
| Parallel and k-Parallel Submanifolds | p. 33 |
| Examples: Segre and Plucker Submanifolds | p. 36 |
| Example: Veronese Submanifold | p. 40 |
| Parallel Submanifolds and the Gauss Map | p. 43 |
| Parallel Submanifolds and Local Extrinsic Symmetry | p. 44 |
| Complete Parallel Irreducible Submanifolds as Standard Imbedded Symmetric R-Spaces | p. 46 |
| Semiparallel Submanifolds | p. 51 |
| The Semiparallel Condition and Its Special Cases | p. 51 |
| The Semiparallel Condition from the Algebraic Viewpoint | p. 54 |
| Decomposition of Semiparallel Fundamental Triplets | p. 57 |
| Triplets of Large Principal Codimension | p. 59 |
| Semiparallel Submanifolds as Second-Order Envelopes of Parallel Submanifolds | p. 63 |
| Second-Order Envelope of Segre Submanifolds | p. 66 |
| A New Approach to Veronese Submanifolds | p. 70 |
| Normally Flat Semiparallel Submanifolds | p. 73 |
| Principal Curvature Vectors and the Semiparallel Condition | p. 73 |
| Normally Flat Parallel Submanifolds | p. 75 |
| Adapted Frame Bundle for a Second-Order Envelope | p. 78 |
| Second-Order Envelope as Warped Product | p. 80 |
| Semiparallel Submanifolds of Principal Codimension 1 | p. 84 |
| Semiparallel Submanifolds of Principal Codimension 2 in Euclidean Space | p. 89 |
| Normally Flat Semiparallel Submanifolds of Principal Codimension 2 in Non-Euclidean Space Forms | p. 93 |
| Semiparallel Surfaces | p. 97 |
| Semiparallel Spacelike Surfaces | p. 97 |
| The Case of Regular Metrics | p. 99 |
| Veronese Surfaces | p. 101 |
| Second-Order Envelopes of Veronese Surfaces | p. 106 |
| The Case of a Singular Metric | p. 108 |
| The subcases where span{A, B} has singular metric | p. 109 |
| The subcases where span{A, B} has regular metric | p. 112 |
| Semiparallel Timelike Surfaces in Lorentz Spacetime Forms | p. 114 |
| The principal case | p. 115 |
| The exceptional case | p. 119 |
| Spacelike 2-Parallel Surfaces | p. 123 |
| q-Parallel Surfaces as Semiparallel Surfaces | p. 130 |
| Semiparallel Three-Dimensional Submanifolds | p. 135 |
| Semiparallel Submanifolds M[superscript 3] of Principal Codimension m[subscript 1] [less than or equal] 2 | p. 135 |
| Nonminimal Semiparallel M[superscript 3] of Principal Codimension m[subscript 1] = 3 | p. 138 |
| Semiparallel M[superscript 3] of Principal Codimension m[subscript 1] = 4 | p. 147 |
| Higher Principal Codimensions: Conclusions | p. 154 |
| Decomposition Theorems | p. 157 |
| Decomposition of Semiparallel Submanifolds | p. 157 |
| Decomposition of Parallel Submanifolds | p. 162 |
| Decomposition of Normally Flat 2-Parallel Submanifolds | p. 164 |
| Structure of Submanifolds with Flat van der Waerden-Bortolotti Connection | p. 168 |
| Umbilic-Likeness of Main Symmetric Orbits | p. 175 |
| Two Kinds of Symmetric Orbits | p. 175 |
| Umbilic-Likeness of Plucker Orbits | p. 178 |
| Unitary Orbits of the Plucker Action | p. 181 |
| Umbilic-Likeness of Unitary Orbits | p. 184 |
| The Segre Action and Its Symmetric Orbits | p. 195 |
| The Veronese Action and Its Symmetric Orbits | p. 197 |
| The Problem of Umbilic-Likeness of Veronese Orbits | p. 201 |
| Umbilic-Likeness of Veronese-Grassmann Orbits | p. 205 |
| Detailed Analysis of a Model Case | p. 214 |
| Geometric Descriptions in General | p. 219 |
| Products of Umbilic-Like Orbits | p. 219 |
| General Semiparallel Submanifolds and Their Adapted Frame Bundles | p. 223 |
| Warped Products and Immersed Fibre Bundles | p. 227 |
| Semiparallel Submanifolds of Cylindrical or Toroidal Segre Type | p. 229 |
| The case of umbilic-like Segre orbits | p. 230 |
| The case of nonumbilic-like Segre orbits | p. 235 |
| Isometric Semiparallel Immersions of Riemannian Manifolds of Conullity Two | p. 237 |
| Semiparallel Submanifolds with Plane Generators of Codimension 2 | p. 237 |
| Some Particular Cases | p. 241 |
| Semiparallel Manifolds of Conullity Two in General | p. 242 |
| Some Generalizations | p. 249 |
| k-Semiparallel Submanifolds | p. 249 |
| On 2-Semiparallel Submanifolds | p. 252 |
| 2-Semiparallel Surfaces in Space Forms | p. 253 |
| Recurrent and Pseudoparallel Submanifolds | p. 261 |
| Submanifolds with Semiparallel Tensor Fields | p. 263 |
| Examples: The Surfaces | p. 266 |
| H-semiparallel and H-parallel surfaces | p. 267 |
| R[superscript perpendicular, bottom]-parallel surfaces | p. 270 |
| R- or Ric-parallel surfaces | p. 271 |
| T-semiparallel surfaces | p. 271 |
| Ric-Semiparallel Hypersurfaces and Ryan's Problem | p. 272 |
| Extended Ryan's Problem for Normally Flat Submanifolds | p. 279 |
| R-Semiparallel but Not Semiparallel Normally Flat Submanifolds of Codimension 2 | p. 282 |
| References | p. 287 |
| Index | p. 303 |
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