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Do Carmo's main research interests were Riemannian geometry and the differential geometry of surfaces. [3]In particular, he worked on rigidity and convexity of isometric immersions, [26] [27] stability of hypersurfaces [28] [29] and of minimal surfaces, [30] [31] topology of manifolds, [32] isoperimetric problems, [33] minimal submanifolds of a sphere, [34] [35] and manifolds of constant mean ...
In differential geometry, Hilbert's theorem (1901) states that there exists no complete regular surface of constant negative gaussian curvature immersed in . This theorem answers the question for the negative case of which surfaces in can be obtained by isometrically immersing complete manifolds with constant curvature .
Selim G. Akl (Ph.D., McGill University, born 1978) is a professor at Queen's University in the Queen's School of Computing, where he leads the Parallel and Unconventional Computation Group. [1] His research interests are primarily in the area of algorithm design and analysis, in particular for problems in parallel computing and unconventional ...
Differential geometry has applications to both Lagrangian mechanics and Hamiltonian mechanics. Symplectic manifolds in particular can be used to study Hamiltonian systems. Riemannian geometry and contact geometry have been used to construct the formalism of geometrothermodynamics which has found applications in classical equilibrium thermodynamics.
Darboux frame. In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame as applied to surface geometry. A Darboux frame exists at any non- umbilic point of a surface embedded in Euclidean space. It is named after French mathematician Jean Gaston ...
The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. [1][2][3] Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental ...
Pearson Education, known since 2011 as simply Pearson, is the educational publishing and services subsidiary of the international corporation Pearson plc. The subsidiary was formed in 1998, when Pearson plc acquired Simon & Schuster 's educational business and combined it with Pearson's existing education company Addison-Wesley Longman. [1]
Researchers in structural geology use the Lambert azimuthal projection to plot crystallographic axes and faces, lineation and foliation in rocks, slickensides in faults, and other linear and planar features. In this context the projection is called the equal-area hemispherical projection. There is also an equal-angle hemispherical projection ...