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Shoshichi Kobayashi
was a Japanese mathematician. He was the eldest brother of electrical engineer and computer scientist Hisashi Kobayashi. His research interests were in Riemannian and complex manifolds, transformation groups of geometric structures, and Lie algebras. Biography Kobayashi graduated from the University of Tokyo in 1953. In 1956, he earned a Ph.D. from the University of Washington under Carl B. Allendoerfer. His dissertation was ''Theory of Connections''. He then spent two years at the Institute for Advanced Study and two years at MIT. He joined the faculty of the University of California, Berkeley in 1962 as an assistant professor, was awarded tenure the following year, and was promoted to full professor in 1966. Kobayashi served as chairman of the Berkeley Mathematics Department for a three-year term from 1978 to 1981 and for the 1992 Fall semester. He chose early retirement under the VERIP plan in 1994. The two-volume book ''Foundations of Differential Geometry'', which he coau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berkeley, California
Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Irish bishop and philosopher George Berkeley. It borders the cities of Oakland and Emeryville to the south and the city of Albany and the unincorporated community of Kensington to the north. Its eastern border with Contra Costa County generally follows the ridge of the Berkeley Hills. The 2020 census recorded a population of 124,321. Berkeley is home to the oldest campus in the University of California System, the University of California, Berkeley, and the Lawrence Berkeley National Laboratory, which is managed and operated by the university. It also has the Graduate Theological Union, one of the largest religious studies institutions in the world. Berkeley is considered one of the most socially progressive cities in the United States. History Indigenous history The site of today's City of Berkeley was the territo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Manifold
In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in \mathbb^n, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. Implications of complex structure Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds. For example, the Whitney embedding theorem tells us that every smooth ''n''-dimensional manifold can be embedded as a smooth submanifold of R2''n'', whereas it is "rare" for a complex manifold to have a holomorphic embedding into C''n''. Consider for example any compact connected complex manifold ''M'': any holomorphic function on it is cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Simons
James Harris Simons (; born 25 April 1938) is an American mathematician, billionaire hedge fund manager, and philanthropist. He is the founder of Renaissance Technologies, a quantitative hedge fund based in East Setauket, New York. He and his fund are known to be quantitative investors, using mathematical models and algorithms to make investment gains from market inefficiencies. Due to the long-term aggregate investment returns of Renaissance and its Medallion Fund, Simons is described as the "greatest investor on Wall Street," and more specifically "the most successful hedge fund manager of all time." As reported by ''Bloomberg Billionaires Index'', Simons' net worth is estimated to be $25.2 billion, making him the 66th-richest person in the world. Simons is known for his studies on pattern recognition. He developed the Chern–Simons form (with Shiing-Shen Chern), and contributed to the development of string theory by providing a theoretical framework to combine geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariant Derivative
In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection. In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean directional derivative onto the manifold's tangent space. In this case the Euclidean derivative is broken into two parts, the extrinsic normal component (dependent on the embedding) and the intrinsic covariant derivative component. The name is motivated by the importance of changes of coordinate in physics: the covariant derivative transforms covariantly under a general coordinate transformation, that is, linearly via the Jacobia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss–Codazzi Equations
In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi Formulas) are fundamental formulas which link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold. The equations were originally discovered in the context of surfaces in three-dimensional Euclidean space. In this context, the first equation, often called the Gauss equation (after its discoverer Carl Friedrich Gauss), says that the Gauss curvature of the surface, at any given point, is dictated by the derivatives of the Gauss map at that point, as encoded by the second fundamental form. The second equation, called the Codazzi equation or Codazzi-Mainardi equation, states that the covariant derivative of the second fundamental form is fully symmetric. It is named for Gaspare Mainardi (1856) and Delfino Codazzi (1868 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connection (principal Bundle)
In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal ''G''-connection on a principal G-bundle ''P'' over a smooth manifold ''M'' is a particular type of connection which is compatible with the action of the group ''G''. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection. It gives rise to (Ehresmann) connections on any fiber bundle associated to ''P'' via the associated bundle construction. In particular, on any associated vector bundle the principal connection induces a covariant derivative, an operator that can differentiate sections of that bundle along tangent directions in the base manifold. Principal connections generalize to arbitrary principal bundles the concept of a linear connection on the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nice
Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly 1 millionDemographia: World Urban Areas , Demographia.com, April 2016 on an area of . Located on the , the southeastern coast of France on the , at the foot of the |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Katsumi Nomizu
was a Japanese-American mathematician known for his work in differential geometry. Life and career Nomizu was born in Osaka, Japan on the first day of December, 1924. He studied mathematics at Osaka University, graduating in 1947 with a Master of Science then traveled to the United States on a U.S. Army Fulbright Scholarship. He studied first at Columbia University and then at the University of Chicago where in 1953 he became the first student to earn a Ph.D. under the thesis direction of Shiing-Shen Chern. The subject was affine differential geometry, a topic to which he would return much later in his career. He presented his thesis, ''Invariant affine connections on homogeneous spaces'' in 1953. Returning to Japan, he studied at Nagoya University, obtaining a doctor of science in 1955. He published his first volume, ''Lie Groups and Differential Geometry'' dedicated to his wife Kimiko whom he had married that same year. Nomizu taught at Nagoya University until 1958 when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Differential Geometry
''Foundations of Differential Geometry'' is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu. The first volume was published in 1963 and the second in 1969, by Interscience Publishers. Both were published again in 1996 as Wiley Classics Library. The first volume considers manifolds, fiber bundles, tensor analysis, connections in bundles, and the role of Lie groups. It also covers holonomy, the de Rham decomposition theorem and the Hopf–Rinow theorem. According to the review of James Eells, it has a "fine expositional style" and consists of a "special blend of algebraic, analytic, and geometric concepts". Eells says it is "essentially a textbook (even though there are no exercises)". An advanced text, it has a "pace geared to a neterm graduate course". The second volume considers submanifolds of Riemannian manifolds, the Gauss map, and the second fundamental form. It continues with geodesics on Riemannian man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholars, including J. Robert Oppenheimer, Albert Einstein, Hermann Weyl, John von Neumann, and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research is never contracted or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Washington
The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle approximately a decade after the city's founding. The university has a 703 acre main campus located in the city's University District, as well as campuses in Tacoma and Bothell. Overall, UW encompasses over 500 buildings and over 20 million gross square footage of space, including one of the largest library systems in the world with more than 26 university libraries, art centers, museums, laboratories, lecture halls, and stadiums. The university offers degrees through 140 departments, and functions on a quarter system. Washington is the flagship institution of the six public universities in Washington state. It is known for its medical, engineering, and scientific research. Washington is a member of the Association of American Universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
