Born on 12 January in Lugo in what is now Italy, Gregorio Ricci-Curbastro was a mathematician best known as the inventor of tensor. According to our current on-line database, Gregorio Ricci-Curbastro has 1 student and descendants. We welcome any additional information. If you have. Gregorio Ricci-Curbastro Source for information on Gregorio Ricci- Curbastro: Science and Its Times: Understanding the Social Significance of.
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He is most famous as the inventor of tensor calculusbut also published important works in other fields. With his former student Tullio Levi-Civitahe wrote his most famous single publication,  a pioneering work on the calculus of tensorssigning it as Gregorio Ricci.
This appears to be the only time that Ricci-Curbastro used the shortened form of his name in a publication, and gregrio to cause confusion. Ricci-Curbastro also published important works in other fields, including a book on higher algebra and infinitesimal analysis,  and papers on the theory of real numbersan area in which he extended the research begun by Richard Dedekind.
Completing privately his high school studies at only sixteen years of age he enrolled on the course of philosophy-mathematics at Rome University The following year the Papal State fell and gregorjo Gregorio was called by his father to the city of his birth, Lugo.
Gregorio Ricci-Curbastro |
Subsequently he attended courses at Bologna, but after only one durbastro he enrolled at the Scuola Normale Superiore di Pisa. In Ricci-Curbastro obtained a scholarship at the Technische Hochschule of MunichBavaria, and he later worked as an assistant of Ulisse Dini, his teacher. In he became a lecturer of mathematics at the University of Padua where he dealt with Riemannian geometry and differential quadratic forms.
He formed a research group in which Tullio Levi-Civita worked, with whom he wrote the fundamental treatise on absolute differential calculus also known as Ricci calculus with coordinates or tensor calculus on Riemannian manifold, which then became the lingua franca of the subsequent theory of Einstein ‘s general relativity. In fact absolute differential calculus had a crucial role in developing the theory, as is shown in a letter written by Albert Einstein to Ricci-Curbastro’s nephew.
In this context Ricci-Curbastro identified the so-called Ricci tensor which would have a crucial role within that theory. The advent of tensor calculus in dynamics goes back to Lagrangewho originated the general treatment of a dynamical systemand to Riemannwho was the first to think about geometry in an arbitrary number of dimensions.
He was also influenced by the works of Christoffel and of Lipschitz on the quadratic forms. He participated actively ricck political life, both in his native town and in Padua, and contributed with his projects to the Ravenna-area land drainage and the Lugo aqueduct. An asteroidRicciis named after him. He is most famous as the inventor of tensor calculus, but also published important works in other fields.
With his former student Tullio Levi-Civita, he wrote his most famous single publication, a pioneering work on the calculus of tensors, signing it as Gregorio Ricci. Ricci-Curbastro also published important crbastro in other fields, including a book on higher algebra and infinitesimal analysis, and papers on the theory of real numbers, an area in which he extended the research begun by Richard Dedekind.
The following year the Papal State fell curbwstro so Gregorio was called In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a narrow conical piece of a small geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.
As such, it provides one way of measuring the degree to which the geometry determined by a given Riemannian metric might differ from that of ordinary Euclidean n-space. The Ricci tensor grsgorio defined on any pseudo-Riemannian manifold, as a trace of the Riemann curvature tensor. Like the metric itself, the Ricci tensor is a symmetric bilinear form on the tangent space of the manifold Bessep.
Gregorio Ricci-Curbastro | Revolvy
It is related to the matter content of the universe by means of the Einstein field equation. In differential geometry, lower bounds on the Ri Several stages of Ricci flow on a 2D manifold.
In differential geometry, the Ricci flowItalian: It is a process that deforms the metric of a Riemannian manifold in a way formally analogous to the diffusion of heat, smoothing out irregularities in the metric. Hamilton in and is also referred to as the Ricci—Hamilton flow.
If we consider the metric tensor and the associated Ricci tensor to be functions of In mathematics, tensor calculus or tensor analysis is an extension of vector calculus to tensor fields tensors that may vary over a manifold, e. Contrasted with the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold.
Tensor calculus has many real-life applications in physics and engineering, including elasticity, continuum mechanics, electromagnetism see mathematical descriptions of the electromagnetic fieldgeneral relativity see mathematics of general relativity ,quantum field theory. Retrieved 17 May Geographical distribution As of In Italy, the frequency of the surname was higher than national average 1: Santa Fe Province 1: Buenos Aires Province 1: In grwgorio, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields.
Jan Arnoldus Schouten developed the modern notation and formalism for this mathematical gregoriio, and made contributions to the theory, during its applications to general relativity and differential geometry in the early twentieth century.
The tensor is the sum of its components multiplied by their corresponding basis elements. Tensors and tensor fields can be expressed in terms of their components, and operations on tensors and tensor fields can be expressed in terms of operations on their components. He was xurbastro pupil of Gregorio Curbaztro, the inventor of tensor calculus. His work included foundational papers in both pure and applied mathematics, celestial mechanics notably on the three-body problemanalytic mechanics the Levi-Civita separability conditions in the Hamilton—Jacobi equation  and hydrodynamics.
He graduated in from the University of Padua Faculty of Mathematics. In he earned a teaching diploma after which he was appointed to the Faculty of Science teacher’s college in Pavia.
In he was appointed to the Padua C Gregorio is a masculine given name and a surname. It may refer to: Araneta —Filipino lawyer, businessman and nationalist Gregorio Benito bornSpanish retired footballer Gregorio C. Brillantes, Filipino writer Gregorio di Cecco c. The second-order Cauchy gregorip tensor in the basis e, e, e: In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors v and w at a point of a surface or higher dimensional differentiable manifold and produces a real number scalar g v, w in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.
In the same rifci as a dot product, metric tensors are used to define the length of and angle between tangent vectors. Through cuebastro, the metric tensor allows one to define and compute the length of curves on the manifold. A manifold equipped with curbstro positive-definite metric tensor is known as a Riemannian manifold.
On a Riemannian manifold, the curve connecting two curvastro that locally has the smallest length is called a geodesic, and its length is the distance that a passenger in the manifold needs to traverse to go from one point John “Jack” Marshall Lee born 2 September is an American mathematician, specializing in differential geometry.
He continued his studies at Tufts University in — At the University of Washington he became in an assistant professor, in an associate professor, and in a full professor. He died in the Theresienstadt concentration camp. Today he is best known for Pick’s theorem for determining the area of lattice polygons. He published it in an article in ; it was popularized when Hugo Dyonizy Steinhaus included it in the edition of Mathematical Snapshots.
Pick studied at the University of Vienna and defended his Ph. After receiving his doctorate he was appointed an assistant to Ernst Mach at the Charles-Ferdinand University in Prague. He became a lecturer there in He took a leave from the university in during which he worked with Felix Klein at the University of Leipzig.
Other than that year, he remained in Prague until his retirement in at which time he returned to Vienna. Pick headed the committee at the then German university of Prague which appoin In mathematics, multilinear algebra extends the methods of linear algebra.
Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of p-vectors and multivectors with Grassmann algebra. Origin In a vector space of dimension n, one usually considers only the vectors. According to Hermann Grassmann and others, this presumption misses the complexity of considering the structures of pairs, triples, and general multivectors. Since there are several combinatorial possibilities, the space of multivectors turns out to have 2n dimensions.
The abstract formulation of the determinant is the most immediate application. Multilinear algebra also has applications in mechanical study of material response to stress and strain with various moduli of elasticity. This practical reference led to the use of the word tensor to describe the elements of the multilinear space. The extra structure in a multilinear space has led it to play an import In differential geometry, a Ricci soliton is a special type of Riemannian metric.
Such metrics evolve under Ricci flow only by symmetries of the flow, and they can be viewed as generalizations of Einstein metrics.
Ricci flow solutions are invariant under diffeomorphisms and scaling, so one is led to consider solutions that evolve exactly in these ways. Elwin Bruno Christoffel German: He introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus, which would later provide the mathematical basis for general relativity.
Life Christoffel was born on 10 November in Montjoie now Monschau in Prussia in a family of cloth merchants. He was initially educated at home in languages and mathematics, then attended the Jesuit Gymnasium and the Friedrich-Wilhelms Gymnasium in Cologne. In he went to the University of Berlin, where he studied mathematics with Gustav Dirichlet which had a strong influence over him  among others, as well as attending courses in physics and chemistry.
He received his doctorate in Berlin in for a thesis on the motion of electricity in homogeneous bodies written under the supervision of Martin Ohm, Ernst Kummer and Heinrich Gustav Magnus.
Eugenio Beltrami 16 November — 18 February was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami—Klein model.
He also developed singular value decomposition for matrices, which has been subsequently rediscovered several times. Beltrami’s use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita. He began studying mathematics at University of Pavia inbut was expelled from Ghislieri College in due to his political opinions—he was sympathetic with the Risorg A nondifferentiable atlas of charts for the globe.
The results of calculus may not be compatible between charts if the atlas is not differentiable. In the center and right charts, the Tropic of Cancer is a smooth curve, curhastro in the left chart it has a sharp corner. The notion of a differentiable manifold refines that of a manifold by requiring the functions that transform between charts to be differentiable.
In mathematics, a differentiable manifold also differential manifold is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.