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F Tricerri

Other affiliations: University of Turin
Bio: F Tricerri is an academic researcher from University of Florence. The author has contributed to research in topics: Sectional curvature & Riemann curvature tensor. The author has an hindex of 13, co-authored 21 publications receiving 1139 citations. Previous affiliations of F Tricerri include University of Turin.

Papers
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Book
29 Jul 1983
TL;DR: The main aim of as discussed by the authors is to give a classification of homogeneous Riemannian structures on a manifold, and some of these are discussed in detail, with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics.
Abstract: The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail.Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

227 citations

Journal ArticleDOI
TL;DR: Some natural metrics on the tangent and on the sphere tangent bundle of Riemannian manifold were constructed and studied via the moving frame method in this article, and some natural metrics were constructed on the manifold manifold on the basis of these metrics.
Abstract: Some «natural» metrics on the tangent and on the sphere tangent bundle of Riemannian manifold are constructed and studied via the moving frame method.

138 citations

Journal ArticleDOI
TL;DR: In this paper, the authors give examples of Lorentz manifolds modelled on an indecomposable Lévy symmetric space which are geodesically complete and not locally homogeneous.

105 citations


Cited by
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Book
01 Feb 1993
TL;DR: Inequalities for mixed volumes 7. Selected applications Appendix as discussed by the authors ] is a survey of mixed volumes with bounding boxes and quermass integrals, as well as a discussion of their applications.
Abstract: 1. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.

3,954 citations

Journal ArticleDOI
Robin Forman1
TL;DR: In this article, a discrete Morse theory for CW complexes is presented, which can be used to give a Morse theoretic proof of the Poincare conjecture in dimension 5, along the lines of the proof in [Mi2] along with discrete analogues of such intrinsically smooth notions as the gradient vector field and the gradient flow associated to a Morse function.

1,046 citations

Journal ArticleDOI
TL;DR: An overview of some of the better known quantization techniques for systems with finite numbers of degrees-of-freedom can be found in this paper, including canonical quantization and the related Dirac scheme, introduced in the early days of quantum mechanics.
Abstract: This survey is an overview of some of the better known quantization techniques (for systems with finite numbers of degrees-of-freedom) including in particular canonical quantization and the related Dirac scheme, introduced in the early days of quantum mechanics, Segal and Borel quantizations, geometric quantization, various ramifications of deformation quantization, Berezin and Berezin–Toeplitz quantizations, prime quantization and coherent state quantization. We have attempted to give an account sufficiently in depth to convey the general picture, as well as to indicate the mutual relationships between various methods, their relative successes and shortcomings, mentioning also open problems in the area. Finally, even for approaches for which lack of space or expertise prevented us from treating them to the extent they would deserve, we have tried to provide ample references to the existing literature on the subject. In all cases, we have made an effort to keep the discussion accessible both to physicists and to mathematicians, including non-specialists in the field.

257 citations