O'Neill, Barrett. <br/><br/>
Elementary differential geometry /  
Barrett O'Neill. 
 - Rev. 2nd ed. 
 - Amsterdam :  Boston :  Elsevier Academic Press,  c2006. 
 - xi, 503 p.   ill. ;  24 cm. 
<br/><br/> Includes bibliographical references (p. 467) and index. 
<br/><br/>Introduction <br/><br/>Chapter 1: calculus on euclidean space: <br/>Euclidean space. Tangent vectors. Directional derivatives. Curves in r3. 1-forms. Differential forms. Mappings;<br/><br/>Chapter 2: frame fields: <br/>Dot product. Curves. The frenet formulas. Arbitraryspeed curves. Covariant derivatives. Frame fields. Connection forms. The structural equations. ;<br/><br/>Chapter 3: euclidean geometry: <br/>Isometries of r3. The tangent map of an isometry. Orientation. Euclidean geometry. Congruence of curves. ;<br/><br/>Chapter 4: calculus on a surface: <br/>Surfaces in r3. Patch computations. Differentiable functions and tangent vectors. Differential forms on a surface. Mappings of surfaces. Integration of forms. Topological properties. Manifolds.;<br/><br/>Chapter 5: shape operators: <br/>The shape operator of m r3. Normal curvature. Gaussian curvature. Computational techniques. The implicit case. Special curves in a surface. Surfaces of revolution. ;<br/><br/>Chapter 6: geometry of surfaces in r3:<br/>The fundamental equations. Form computations. Some global theorems. Isometries and local isometries. Intrinsic geometry of surfaces in r3. Orthogonal coordinates. Integration and orientation. Total curvature. Congruence of surfaces. ;<br/><br/>Chapter 7: riemannian geometry: geometric surfaces. Gaussian curvature. Covariant derivative. Geodesics. Clairaut parametrizations. The gauss-bonnet theorem. Applications of gauss-bonnet. ;<br/><br/>Chapter 8: global structures of surfaces: length-minimizing properties of geodesics. Complete surfaces. Curvature and conjugate points. Covering surfaces. Mappings that preserve inner products. Surfaces of constant curvature. Theorems of bonnet and hadamard. ;<br/><br/>Appendix <br/><br/>Bibliography <br/><br/>Answers to odd-numbered exercises <br/><br/>Subject index<br/> 
<br/><br/><label>ISBN: </label>0120887355 (acidfree paper) 9780120887354 (hbk) 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Geometry, Differential.
<br/><br/><label>Dewey Class. No.: </label>516.36  / N411