ANNOUNCEMENTS
MTH 675 - Fall 2005

11/17/05

Instructions for using the other software I demonstrated last week are finally available, and can be found here.

A further discussion of the Hodge dual operator can be found here.

11/16/05

A further discussion of the divergence and the Divergence Theorem can be found in a paper I wrote, which can be found here.

11/14/05

Some notes on curvature can be found here.

11/9/05

Instructions for using using the software package I demonstrated today (SHEEP) at OSU can be found here.

SHEEP is in principle freely available, although the underlying PSL (lisp) license requires that copies be obtained individually. The website is currently unavailable, but I would be happy to relay requests. I know there is a version for Linux (and most other flavors of UNIX, possibly including cygwin), and I'm pretty sure there's also a DOS version.

I am still trying to track down information about Maple and Mathematica access through COSINe — it doesn't help that the relevant machine crashed today. I will post further information as soon as possible.

The site I tried to find at the end of class, which could do "live" tensor calculations, was called GRlite, and appears to have been taken out of service.

11/4/05

The Pacific Northwest Geometry Seminar will meet at OSU this weekend. Further information is available here. (There is no registration fee to attend this meeting.)

One of the speakers is Nathan Dunsfield, a former OSU math major, who will also give next week's colloquium.

11/1/05

A JAVA applet demonstrating parallel transport on the sphere can be found here.

10/31/05

An annotated book list for relativity can be found here. The most accessible description of the Schwarzschild solution is the one in d'Inverno, who however uses slightly different conventions for the Kruskal-Szekeres coordinates.

An intersting site with information about black holes can be found here. The material closest to today's lecture is in Section 5.

10/24/05

Here are some links to the materials I referred to in class today:

2-dimensional rotations

3-dimensional rotations

Foucault Pendulum

Earth Hockey    (see also the listing at the National Curve Bank, which can be found here)

10/20/05

I will be giving a guest lecture next Tuesday, 10/25, in CS 554: Geometry Modeling and Computer Graphics, which meets in Wiegand 132 from 9-10:20 AM. The lecture will discuss the curvature of curves and surfaces in three dimensions.

10/13/05

O'Neill is now also on reserve at the library.

10/7/05

A copy of Bishop & Goldberg is now on reserve at the library. A copy of O'Neill will be added as soon as possible.

10/6/05

Further discussion of the geometry of special relativity can be found at this website. Comments on this manuscript would be welcome; I hope to publish it some day.

9/30/05

Further discussion of the canonical isomorphism between vectors and dual vectors (the maps I called "sharp" and "flat") can be found in O'Neill: Proposition 10 on page 60, and the discussion of contraction beginning at the bottom of page 81. Note that these discussions are embedded in sections which treat some topics we haven't had yet, such as covariant differentiation (connections) and curvature.

9/28/05

An introduction to the properties of the metric tensor can be found in Bishop and Goldberg §2.20-§2.21. Similar material is in Boothby §V.2. However, I could not find a reference in either text to the isomorphism induced by the metric tensor between tensors of the same rank (e.g. 1), but different types (e.g. vectors and covectors). We will discuss this isomorphism further on Friday.