Search results for "levi-civita"

Toward a scientific and personal biography of Tullio Levi-Civita (1873–1941)

2005

International audience; Tullio Levi-Civita was one of the most important Italian mathematicians in the early part of the 20th century, contributing significantly to a number of research fields in mathematics and physics. In addition, he was involved in the social and political life of his time and suffered severe political and racial persecution during the period of Fascism. He tried repeatedly and in several cases successfully to help colleagues and students who were victims of anti-Semitism in Italy and Germany. His scientific and private life is well documented in the letters and documents contained in his Archive. The authors' aim is to illustrate the events of his life by means of his …

The Riemannian manifold of all Riemannian metrics

1991

In this paper we study the geometry of (M, G) by using the ideas developed in [Michor, 1980]. With that differentiable structure on M it is possible to use variational principles and so we start in section 2 by computing geodesics as the curves in M minimizing the energy functional. From the geodesic equation, the covariant derivative of the Levi-Civita connection can be obtained, and that provides a direct method for computing the curvature of the manifold. Christoffel symbol and curvature turn out to be pointwise in M and so, although the mappings involved in the definition of the Ricci tensor and the scalar curvature have no trace, in our case we can define the concepts of ”Ricci like cu…

Some remarks on minimal surfaces in riemannian manifolds

1970

Feuilletages Riemanniens singuliers

2006

Abstract We prove that a singular foliation on a compact manifold admitting an adapted Riemannian metric for which all leaves are minimal must be regular. To cite this article: V. Miquel, R.A. Wolak, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The role of virtual work in Levi-Civita's parallel transport

2015

International audience; According to current history of science, Levi-Civita introduced parallel transport solely to give a geometrical interpretation to the covariant derivative of absolute differential calculus. Levi-Civita, however, searched a simple computation of the curvature of a Riemannian manifold, basing on notions of the Italian school of mathematical physics of his time: holonomic constraints, virtual displacements and work, which so have a remarkable, if not dominant, role in the origin of parallel transport.