The tangent frame bundle (or simply the frame bundle) of a smooth manifold M is the frame bundle associated to the tangent bundle of M. The frame bundle of M is often denoted FM or GL(M) rather than F(TM). If M is n-dimensional then the tangent bundle has rank n, so the frame bundle of M is a principal GLn(R) bundle over M.
Read more about this topic: Frame Bundle
Famous quotes containing the words frame and/or bundle:
“The heroes and discoverers have found true more than was previously believed, only when they were expecting and dreaming of something more than their contemporaries dreamed of, or even themselves discovered, that is, when they were in a frame of mind fitted to behold the truth. Referred to the worlds standard, they are always insane. Even savages have indirectly surmised as much.”
—Henry David Thoreau (18171862)
“In the quilts I had found good objectshospitable, warm, with soft edges yet resistant, with boundaries yet suggesting a continuous safe expanse, a field that could be bundled, a bundle that could be unfurled, portable equipment, light, washable, long-lasting, colorful, versatile, functional and ornamental, private and universal, mine and thine.”
—Radka Donnell-Vogt, U.S. quiltmaker. As quoted in Lives and Works, by Lynn F. Miller and Sally S. Swenson (1981)