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Ravindra Shripad 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). The conjecture is named for Hyman Bass and Daniel Quillen, who formulated the c ... References External links *Directory page at University of MichiganAuthor profilein the database zbMATH {{DEFAUL ...: * *with Krishnendu Gongopadhyay: as editor * with Ulrich Pinkall: References External linksConformal Geometry and Riemann Surfaces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
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 differential calculus, integral 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] |
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_ + 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shlomo Sternberg
Shlomo Zvi Sternberg (born 1936), is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. Education and career Sternberg earned his PhD in 1955 from Johns Hopkins University, with a thesis entitled "''Some Problems in Discrete Nonlinear Transformations in One and Two Dimensions''", supervised by Aurel Wintner. After postdoctoral work at New York University (1956–1957) and an instructorship at University of Chicago (1957–1959), Sternberg joined the Mathematics Department at Harvard University in 1959, where he was George Putnam Professor of Pure and Applied Mathematics until 2017. Since 2017, he is Emeritus Professor at the Harvard Mathematics Department. Among other honors, Sternberg was awarded a List of Guggenheim Fellowships awarded in 1974, Guggenheim fellowship in 1974 and a honorary doctorate by the University of Mannheim in 1991. He delivered the American Mathematical Society, AMS in 1990 and the Hebrew University ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harish-Chandra Research Institute
The Harish-Chandra Research Institute (HRI) is an institution dedicated to research in mathematics and theoretical physics, located in Allahabad (officially Prayagraj), Uttar Pradesh in India. Established in 1975, HRI offers masters and doctoral program in affiliation with the Homi Bhabha National Institute. HRI has a residential campus in Jhusi town near Allahabad on the banks of the River Ganges. The institute has over 30 faculty, 50 doctoral students and 25 post-doctoral visiting research fellows and scientists. HRI is funded by the Department of Atomic Energy (DAE) of the Government of India. History The institute was founded as the Mehta Research Institute of Mathematics and Mathematical Physics in 1975, with an endowment from the B.S. Mehta Trust, Calcutta. The institute was initially managed by Badri Nath Prasad and following his death in January 1966 by S.R. Sinha, both from the Allahabad University. The first official director of the institute was Prabhu Lal Bhatnagar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Institute Of Technology Bombay
The Indian Institute of Technology Bombay (IIT Bombay or IITB) is a public research university and technical institute in Powai, Mumbai, Maharashtra, India. It is considered as one of the best engineering universities in India and is top ranked Indian university in QS World University Rankings 2022 and 3rd in NIRF overall rankings 2022 as well as NIRF engineering rankings 2022. IIT Bombay was founded in 1958. In 1961, the Parliament decreed IITs as Institutes of National Importance. A committee formed by the Government of India recommended the establishment of four higher institutes of technology to set the direction for the development of technical education in the country in 1946. Planning began in 1957 and the first batch of 100 students was admitted in 1958. Since its establishment in Powai, the institute has physically expanded to include more than 584 major buildings with a combined area of more than 2.2 square kilometers. IIT Bombay is considered as one of the foremost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramanujan Mathematical Society
Ramanujan Mathematical Society is an Indian organisation of persons formed with the aim of "promoting mathematics at all levels". The Society was founded in 1985 and registered in Tiruchirappalli, Tamil Nadu, India. Professor G. Shankaranarayanan was the first President, Professor R. Balakrishnan the first Secretary and Professor E. Sampathkumar the first Academic Secretary. The initial impetus for the formation of the Society was the deeply felt need of a new mathematical journal and the necessity of an organisation to launch and nourish the journal. Publications The publications of Ramanujan Mathematical Society include the following: * ''Mathematics Newsletter'': A journal catering to the needs of students, research scholars, and teachers. The Newsletter was launched in the year 1991 with Professor R Balakrishnan as Chief Editor. Currently, Professor S Ponnusamy of IIT Madras is the Chief Editor. *''Journal of the Ramanujan Mathematical Society '': The Journal was started ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyman Bass
Hyman Bass (; born October 5, 1932) MacTutor History of Mathematics archive. Accessed January 31, 2010 is an American , known for work in and in . From 1959 to 1998 he was Professor in the Mathematics Department at |
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 ''Quate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1942 Births
Year 194 ( CXCIV) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Septimius and Septimius (or, less frequently, year 947 ''Ab urbe condita''). The denomination 194 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Emperor Septimius Severus and Decimus Clodius Septimius Albinus Caesar become Roman Consuls. * Battle of Issus: Septimius Severus marches with his army (12 legions) to Cilicia, and defeats Pescennius Niger, Roman governor of Syria. Pescennius retreats to Antioch, and is executed by Severus' troops. * Septimius Severus besieges Byzantium (194–196); the city walls suffer extensive damage. Asia * Battle of Yan Province: Warlords Cao Cao and Lü Bu fight for control over Yan Province; the battle lasts for over 100 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Indian Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman emperor, a ... [...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 differential calculus, integral 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 structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
