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Ravi S. Kulkarni
Ravindra Shripad Kulkarni (born 1942) is an Indian mathematician, specializing in differential geometry. He is known for the Kulkarni–Nomizu product. Education and career Ravi S. Kulkarni received in 1968 his Ph.D. from Harvard University under Shlomo Sternberg with thesis ''Curvature and Metric''. For the academic year 1980–1981 he was a Guggenheim Fellow. He has served as the president of the Ramanujan Mathematical Society. Selected publications * * * * * * *with Allan L. Edmonds & John H. Ewing: *with Allan L. Edmonds & Robert E. Stong: *with Gregory Constantine: *with Hyman Bass Hyman Bass (; born October 5, 1932) [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johns Hopkins University Faculty
Johns may refer to: Places * Johns, Mississippi, an unincorporated community * Johns, Oklahoma, United States, a community * Johns Creek (Chattahoochee River), Georgia, United States * Johns Island (other), islands in Canada and the United States * Johns Mountain, a summit in Georgia * Johns River (other) * Johns Township, Appanoose County, Iowa, United States Other uses * Johns (surname) * Johns Hopkins (1795–1873), American entrepreneur, investor and philanthropist * johns (film), ''johns'' (film), a 1996 film starring David Arquette and Lukas Haas See also * John (other) * Justice Johns (other) * {{disambig, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CUNY Graduate Center Faculty
The City University of New York (CUNY, pronounced , ) is the public university system of New York City. It is the largest urban university system in the United States, comprising 25 campuses: eleven senior colleges, seven community colleges, and seven professional institutions. The university enrolls more than 275,000 students. CUNY alumni include thirteen Nobel Prize winners and twenty-four MacArthur Fellows. The oldest constituent college of CUNY, City College of New York, was originally founded in 1847 and became the first free public institution of higher learning in the United States. In 1960, John R. Everett became the first chancellor of the Municipal College System of New York City, later known as the City University of New York (CUNY). CUNY, established by New York state legislation in 1961 and signed into law by governor Nelson Rockefeller, was an amalgamation of existing institutions and a new graduate school. The system was governed by the Board of Higher Education ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queens College, City University Of New York Faculty
Queens is the largest by area of the Boroughs of New York City, five boroughs of New York City, coextensive with Queens County, in the U.S. state of New York (state), New York. Located near the western end of Long Island, it is bordered by the borough of Brooklyn and by Nassau County, New York, Nassau County to its east, and shares maritime borders with the boroughs of Manhattan, the Bronx, and Staten Island, as well as with New Jersey. Queens is one of the most linguistics, linguistically and ethnically diverse places in the world. With a population of 2,405,464 as of the 2020 United States census, 2020 census, Queens is the second-most populous county in New York state, behind Kings County (Brooklyn), and is therefore also the second-most populous of the five New York City boroughs. If Queens were its own city, it would be the List of United States cities by population, fourth most-populous in the U.S. after the rest of New York City, Los Angeles, and Chicago. Queens is the fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Alumni
The list of Harvard University alumni includes notable graduates, professors, and administrators affiliated with Harvard University. For a list of notable non-graduates of Harvard, see the list of Harvard University non-graduate alumni. For a list of Harvard's presidents, see President of Harvard University. Eight Presidents of the United States have graduated from Harvard University: John Adams, John Quincy Adams, Rutherford B. Hayes, John F. Kennedy, Franklin Delano Roosevelt, Theodore Roosevelt, George W. Bush, and Barack Obama. Bush graduated from Harvard Business School, Hayes and Obama from Harvard Law School, and the others from Harvard College. Over 150 Nobel Prize winners have been associated with the university as alumni, researchers or faculty. Nobel laureates Pulitzer Prize winners ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometers
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Indian Mathematicians
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men ( Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudican re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kulkarni–Nomizu Product
In the mathematical field of differential geometry, the Kulkarni–Nomizu product (named for Ravindra Shripad Kulkarni and Katsumi Nomizu) is defined for two -tensors and gives as a result a -tensor. Definition If ''h'' and ''k'' are symmetric -tensors, then the product is defined via: :\begin (h k)(X_1, X_2, X_3, X_4) := &h(X_1, X_3)k(X_2, X_4) + h(X_2, X_4)k(X_1, X_3) \\ &- h(X_1, X_4)k(X_2, X_3) - h(X_2, X_3)k(X_1, X_4) \\ pt = &\begin h(X_1, X_3) &h (X_1, X_4)\\ k(X_2, X_3) &k (X_2, X_4) \end + \begin k(X_1, X_3) &k (X_1, X_4)\\ h(X_2, X_3) &h (X_2, X_4) \end \end where the ''X''''j'' are tangent vectors and , \cdot, is the matrix determinant. Note that h k = k h, as it is clear from the second expression. With respect to a basis \ of the tangent space, it takes the compact form :(h~\wedge\!\!\!\!\!\!\!\!\;\bigcirc~k)_ = (hk )(\partial_i, \partial_j, \partial_l,\partial_m) = 2h_k_ + 2h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1942 Births
The Uppsala Conflict Data Program project estimates this to be the deadliest year in human history in terms of conflict deaths, placing the death toll at 4.62 million. However, the Correlates of War estimates that the prior year, 1941, was the deadliest such year. Death toll estimates for both 1941 and 1942 range from 2.28 to 7.71 million each. Events Below, the events of World War II have the "WWII" prefix. January * January 1 – WWII: The Declaration by United Nations is signed by China, the United Kingdom, the United States, the Soviet Union, and 22 other nations, in which they agree "not to make any separate peace with the Axis powers". * January 5 – WWII: Two prisoners, British officer Airey Neave and Dutch officer Anthony Luteyn, escape from Colditz Castle in Germany. After travelling for three days, they reach the Swiss border. * January 7 – WWII: ** Battle of Slim River: Japanese forces of the 5th Division (Imperial Japanese Army), 5th Division, sup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulrich Pinkall
Ulrich Pinkall (born 1955) is a German mathematician, specializing in differential geometry and computer graphics. Pinkall studied mathematics at the University of Freiburg with a Diplom in 1979 and a doctorate in 1982 with thesis ''Dupin'sche Hyperflächen'' ( Dupin's hypersurfaces) under the supervision of Martin Barner. Pinkall was then a research assistant in Freiburg until 1984 and from 1984 to 1986 at the Max Planck Institute for Mathematics in Bonn. In 1985 he completed his habilitation in Bonn with thesis ''Totale Absolutkrümmung immersierter Flächen'' (Total absolute curvature of immersed surfaces). Since 1986 he is professor at TU Berlin. In 1985 he received the Otto Hahn Medal of the Max Planck Society. In 1986 he received a ''Heisenberg-Stipendium'' from the Deutsche Forschungsgemeinschaft (DFG). From 1992 to 2003 he was a speaker of the Sonderforschungsbereich (SFB) 288 (differential geometry and quantum physics). In 1998 he was an Invited Speaker with talk ''Qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
