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Diffeomorphometry is the metric study of imagery, shape and form in the discipline of computational anatomy (CA) in medical imaging.The study of images in computational anatomy rely on high-dimensional diffeomorphism groups which generate orbits of the form {}, in which images can be dense scalar magnetic resonance or computed axial tomography images.
A diffeomorphic mapping system is a system designed to map, manipulate, and transfer information which is stored in many types of spatially distributed medical imagery. Diffeomorphic mapping is the underlying technology for mapping and analyzing information measured in human anatomical coordinate systems which have been measured via Medical ...
Every one-dimensional Riemannian manifold is flat. Conversely, given that every connected one-dimensional smooth manifold is diffeomorphic to either or , it is straightforward to see that every connected one-dimensional Riemannian manifold is isometric to one of the following (each with their standard Riemannian structure):
Every complex surface that is diffeomorphic to a K3 surface is a K3 surface, by Robert Friedman and John Morgan. On the other hand, there are smooth complex surfaces (some of them projective) that are homeomorphic but not diffeomorphic to a K3 surface, by Kodaira and Michael Freedman. [9] These "homotopy K3 surfaces" all have Kodaira dimension 1.
From the topological point of view the quaternionic projective line is the 4-sphere, and in fact these are diffeomorphic manifolds. The fibration mentioned previously is from the 7-sphere, and is an example of a Hopf fibration. Explicit expressions for coordinates for the 4-sphere can be found in the article on the Fubini–Study metric.
The numbers tell a clear story for savvy savers. While the latest data shows inflation cooling to 2.4% — its lowest level since February 2021 — today's best certificates of deposit (CDs) are ...
If the Gaussian curvature of a surface M is everywhere positive, then the Euler characteristic is positive so M is homeomorphic (and therefore diffeomorphic) to S 2. If in addition the surface is isometrically embedded in E 3 , the Gauss map provides an explicit diffeomorphism.
From January 2008 to May 2012, if you bought shares in companies when K.C. Turner joined the board, and sold them when she left, you would have a -36.3 percent return on your investment, compared to a -4.2 percent return from the S&P 500.