|
Levi-Civita Symbol, Unit Antisymmetric Symbol , Italian mathematician, wife o ...
Levi-Civita may also refer to: * Tullio Levi-Civita, Italian mathematician ** Levi-Civita connection, the unique affine connection on the tangent bundle of a manifold that preserves the (pseudo-)Riemannian metric and is torsion-free ** Levi-Civita field, a non-Archimedean ordered field ** Levi-Civita parallelogramoid, a quadrilateral in a curved space whose construction generalizes that of a parallelogram in the Euclidean plane ** Levi-Civita symbol, a collection of numbers defined from the sign of a permutation of the natural numbers 1, 2, ..., n, for some positive integer n ** Levi-Civita (crater), a lunar impact crater formation that lies on the far side of the Moon * Libera Trevisani Levi-Civita Libera Trevisani Levi-Civita (17 May 1890 – 11 December 1973) was an Italian mathematician born in Verona. Biography Libera Trevisani earned her classical lyceum A levels in 1908 at the "Bernardino Telesio" Lyceum in Cosenza. In the 1908–190 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tullio Levi-Civita
Tullio Levi-Civita, (; ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus ( tensor calculus) and its applications to the theory of relativity, but who also made significant contributions in other areas. He was a pupil of Gregorio Ricci-Curbastro, the inventor of tensor calculus. His work included foundational papers in both pure and applied mathematics, celestial mechanics (notably on the three-body problem), analytic mechanics (the Levi-Civita separability conditions in the Hamilton–Jacobi equation) and hydrodynamics. Biography Born into an Italian Jewish family in Padua, Levi-Civita was the son of Giacomo Levi-Civita, a lawyer and former senator. He graduated in 1892 from the University of Padua Faculty of Mathematics. In 1894 he earned a teaching diploma after which he was appointed to the Faculty of Science teacher's college in Pavia. In 1898 he was appointed to the Padua Chair of Rational Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Connection
In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold that preserves the ( pseudo-) Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection that satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection. The components (structure coefficients) of this connection with respect to a system of local coordinates are called Christoffel symbols. History The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel. Levi-Civita, along with Gregorio Ricci-Curbastro, used Christoffel's symbols to define the notion of parallel transport and explore the relationship of parallel transport with the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Field
In mathematics, the Levi-Civita field, named after Tullio Levi-Civita, is a non-Archimedean ordered field; i.e., a system of numbers containing infinite and infinitesimal quantities. It is usually denoted \mathcal. Each member a can be constructed as a formal series of the form : a = \sum_ a_q\varepsilon^q , where \mathbb is the set of rational numbers, the coefficients a_q are real numbers, and \varepsilon is to be interpreted as a fixed positive infinitesimal. We require that for every rational number r, there are only finitely many q\in\mathbb less than r with a_q\neq 0; this restriction is necessary in order to make multiplication and division well defined and unique. Two such series are considered equal only if all their coefficients are equal. The ordering is defined according to the dictionary ordering of the list of coefficients, which is equivalent to the assumption that \varepsilon is an infinitesimal. The real numbers are embedded in this field as series in which a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Parallelogramoid
In the mathematical field of differential geometry, the Levi-Civita parallelogramoid is a quadrilateral in a curved space whose construction generalizes that of a parallelogram in the Euclidean plane. It is named for its discoverer, Tullio Levi-Civita. Like a parallelogram, two opposite sides ''AA''′ and ''BB''′ of a parallelogramoid are parallel (via parallel transport side ''AB'') and the same length as each other, but the fourth side ''A''′''B''′ will not in general be parallel to or the same length as the side ''AB,'' although it will be straight (a geodesic).In the article by Levi-Civita (1917, p. 199), the segments AB and A'B ′ are called (respectively) the '' base'' and ''suprabase'' of the parallelogramoid in question. Construction A parallelogram in Euclidean geometry can be constructed as follows: * Start with a straight line segment ''AB'' and another straight line segment ''AA''′. * Slide the segment ''AA''′ along ''AB'' to the end ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers defined from the sign of a permutation of the natural numbers , for some positive integer . It is named after the Italian mathematician and physicist Tullio Levi-Civita. Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations. The standard letters to denote the Levi-Civita symbol are the Greek lower case epsilon or , or less commonly the Latin lower case . Index notation allows one to display permutations in a way compatible with tensor analysis: \varepsilon_ where ''each'' index takes values . There are indexed values of , which can be arranged into an -dimensional array. The key defining property of the symbol is ''total antisymmetry'' in the indices. When any two indices are interchanged, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita (crater)
Levi-Civita is a Lunar craters, lunar impact crater formation that lies on the Far side (Moon), far side of the Moon. It was named after Italian mathematician Tullio Levi-Civita. It is located just to the southwest of the large walled plain Gagarin (crater), Gagarin, and nearly as close to the crater Pavlov (crater), Pavlov to the south-southwest. To the northwest of Levi-Civita lies the smaller crater Pirquet (crater), Pirquet. This is an eroded crater formation with smaller impacts along the rim and within the interior. The southern rim closest to Pavlov is the most eroded section, with multiple small craterlets along the edge and near the inner wall. Along the eastern rim is the satellite crater Levi-Civita F. The interior floor, although relatively level, is pitted by a number of small craters. There is a central ridge near the midpoint of the crater. Satellite craters By convention these features are identified on lunar maps by placing the letter on the side of the crater m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
