A Panoramic View of Riemannian Geometry.

By R. Malley, R. Osserman. 2005

641 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1b6be2953390aa30cc606fc33fdc80a9f372de5c

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Citations in the corpus

Nearly Round Spheres Look Convex (2012, background): “Ever since its introduction by Poincar´e [31], the cut locus has retained some mystery; see Berger [2, Section 6.5.4] for a review.”
An Introduction to Differential Geometry with Applications to Elasticity (2006, methodology): “For detailed treatments, see classic texts such as Choquet-Bruhat, de Witt-Morette & Dillard-Bleick [1977], Marsden & Hughes [1983], Berger [2003], or Gallot, Hulin & Lafontaine [2004].”
Framed bordism and Lagrangian embeddings of exotic spheres (2008, unknown): “11 of [4]), so that (10.”
Differential Geometry and Lie Groups (2020, methodology): “For more examples, consult Gallot, Hulin and Lafontaine [49] (Chapter 2, Section 2C7), Do Carmo [39] (Chapter 13, Section 2) or Berger [14] (Chapter 6).”
A discrete Gauss-Bonnet type theorem (2010, unknown): “Our starting point had been to extend Jacobi fields to the discrete for numerical purposes: for a discretized Jacobi field with smallest space step 1, we have f (0) = f(2)− 2f(1) + f(0) = f(2)− 2f(1).”
Continuous Mesh Framework Part I: Well-Posed Continuous Interpolation Error (2011, background): “Notice that a similar optimal bound of the interpolation error has been proved in [8] for discrete meshes.”
Laplace-Beltrami eigenfunctions for deformation invariant shape representation (2007, unknown): “This stems from completeness of eigenfunctions, which implies the knowledge of Laplace-Beltrami, from which one immediately recovers the metric tensor [Ber03], and so, the isometry class of the surface.”
Karcher means and Karcher equations of positive definite operators (2014, background): “5 of [2]), who showed among other things such a unique minimizer exists if the points all lie in a convex ball in a Riemannian manifold, which is enough to deduce the existence of the least-squares mean globally for P.”
Classification of covariance matrices using a Riemannian-based kernel for BCI applications (2013, background): “Thus, the correct manipulation of these matrices relies on a special branch of differential geometry, namely the Riemannian geometry (Berger, 2003).”
The Restricted Three-Body Problem and Holomorphic Curves (2018, background): “InRiemannian geometry the systole is just the shortest geodesic and there is a huge literature on the subject, see for example [36].”