in "
"
The following are all the errata that I know of. The changes are indicated in red. If you see other errata please send me a message at dwh2@cornell.edu.
These errata were posted on 28 Nov 2004. Some were corrected in the second printing of the first edition and others in the new Revised Edition (2004)
Page ix, line 5-: "*Problem 5.6. Holonomy Explains Foucault's Pendulum"
Page x, line 14-15: Switch the titles of Problems 7.5 and 7.6
Page xvii, line 7-: "ing on-line at http://www.math.cornell.edu/~henderson/books/dg.html. I will"
Page xx, line 14-: "http://www.math.cornell.edu/~dwh/books/dg.html."
Page 5, line 10-: "about 1870 is variously attributed to the French army officer, Charles-Nicolas"
Page 6, Figure 1.5: The short link from the pivot to the rhombus should be of the same length as the distance between the two pivots, but not necessarily the same length as the sides of the rhombus.
Page 38, Figure 2.1: Labels, "distinguishable", "indistinguishable".
Page 43, line 3-6: "such that, for all f.o.v.'s with radius r < d,
|x - p| < r (x within the zoom window),
it is true that
| f (x) - t(x)| < er ( f (x) is indistinguishable from t(x)). "
Page 47, lines 12-22: Change all occurrences of "h" to "b"
Page 48, line 5: "point on non-straight smooth curves? ..."
Page 48, line 18: in the equation replace "h" by "a".
Page 49, line 4: "d. For a smooth planar curve, the magnitude of the curvature is"
Page 49, middle: Change all occurrences of "h" to "b"
Page 52, line 14-: "If g is a smooth curve with nonzero curvature ...".
Page 57, Figure 2.12: The arrowhead on Bp+ should have a point, and the line segment bp+ should be fixed where it disappears under the triangle ap+p- .
Page 58, paragraph after Part b: "To see that "nonzero" is necessary: Take two C-shaped curves with zero curvature at their endpoints, then put these two curves together to form an S-shaped smooth plane curve. This resulting S-shaped has different binormals on the two different pieces."
Page 65, line 17: "2.3 will hold for the intrinsic curvature of curves on a cylinder or on a cone?"
Page 73, line 12- thru 9-: "If a curve C intersects a plane P at a point p, we say that C is tangent to the plane at p, if when we zoom in on p sufficiently [that is, given any tolerance t there is radius r such that in any f.o.v. with radius < r] the portion of the curve in the f.o.v. is indistinguishable from a subset of the plane. But clearly this does not mean that C lies in the plane."
Page 75, Figure 4.2: This figure should be redrawn like Figure 6.1.
Page 82, line 1-: The change is the first
in "
"
Page 89, line 13: "[Hint: Similar to Part b.]"
Page 89, line 11-: "smooth surface M, and Xp a tangent vector in the tangent plane TpM,"
Page 91, line 7 & line 5-: "... = (+1/2 sin 0, -1/2 cos 0, 0) = (0,-1/2,0) = -1/2 ... "
Page 92, lines 10-, 9-, 8-: each line of the equations should be preceeded by a minus sign "-"
Page 108, Problem 2.5: "Prove that every small simple polygon on a sphere and plane ..."
Page 109, line 4-: "see that the line must now be intersecting the polygon at a convex vertex."
Page 111, line 3-: "i. V(s) is a parallel vector field along g as define above."
Page 112, line 8-: "b. If V(s) is a smooth vector field with constant length along the smooth ..."
Page 113, line 5-: "1. Let
and argue that it is perpendicular to the tangent plane"
Page 117, line 6: "For the following problems, it may be helpful to know that the radius"
Page 128, line 8-: "... 5.4.d."
Page 141, line 13-: "a. Show that, for fixed q, the third Taylor approximation"
Page 145, line 1-: "3. Since every curve from p to q must cross C, we have"
Page 146, line 3: The "4." at the beginning of the line should not be bold.
Page 149, line 12: "can be laid flat along a. (Remember that "laid flat" means that the ribbon is tangent to the surface along its center line.)
Page 154, line 5: "... f'(g(a))... "
Page 164, line 10: "d. Compute the geodesic rectangular (or polar) coordinates"
Page 193, line 8: "dependent."
Page 203, line 10: "is a sequence of point pairs {an,bn} such that {an}®y0, {bn}®y0, and f (an) = f (bn), for all n. Let ln"
Page 203, line 13: "bn such that a vector tangent to the graph of f |ln (and, therefore, tangent"
Page 203, line 18: "For an analytic proof of B.3, see [An: Strichartz], Theorem 13.1.2."
Page 203, line 22: "... Then, if the function f(y) = F(x0,y)"
Page 204, line 1-: "C1 m-submanifold of Rn+m."