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Hypercomplex Manifold
In differential geometry, a hypercomplex manifold is a manifold with the tangent bundle equipped with an action by the algebra of quaternions in such a way that the quaternions I, J, K define integrable almost complex structures. If the almost complex structures are instead not assumed to be integrable, the manifold is called quaternionic, or almost hypercomplex. Examples Every hyperkähler manifold is also hypercomplex. The converse is not true. The Hopf surface :\bigg(\backslash 0\bigg)/ (with acting as a multiplication by a quaternion q, , q, >1) is hypercomplex, but not Kähler, hence not hyperkähler either. To see that the Hopf surface is not Kähler, notice that it is diffeomorphic to a product S^1\times S^3, hence its odd cohomology group is odd-dimensional. By Hodge decomposition, odd cohomology of a compact Kähler manifold are always even-dimensional. In fact Hidekiyo Wakakuwa proved that on a compact hyperkähler manifold \ b_\equiv 0 \ mod \ 4. Misha Verbi ... [...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] |
Dominic Joyce
Dominic David Joyce FRS (born 8 April 1968) is a British mathematician, currently a professor at the University of Oxford and a fellow of Lincoln College since 1995. His undergraduate and doctoral studies were at Merton College, Oxford. He undertook a DPhil in geometry under the supervision of Simon Donaldson, completed in 1992. After this he held short-term research posts at Christ Church, Oxford, as well as Princeton University and the University of California, Berkeley in the United States. Joyce is known for his construction of the first known explicit examples of compact Joyce manifolds (i.e., manifolds with G2 holonomy). He has received the London Mathematical Society Junior Whitehead Prize and the European Mathematical Society Young Mathematicians Prize. In 1998 he was an Invited Speaker 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuclear Physics (journal)
''Nuclear Physics A'', ''Nuclear Physics B'', ''Nuclear Physics B: Proceedings Supplements'' and discontinued ''Nuclear Physics'' are peer-reviewed scientific journals published by Elsevier. The scope of ''Nuclear Physics A'' is nuclear and hadronic physics, and that of ''Nuclear Physics B'' is high energy physics, quantum field theory, statistical systems, and mathematical physics. ''Nuclear Physics'' was established in 1956, and then split into ''Nuclear Physics A'' and ''Nuclear Physics B'' in 1967. A supplement series to ''Nuclear Physics B'', called ''Nuclear Physics B: Proceedings Supplements'' has been published from 1987 onwards until 2015 and continues as ''Nuclear and Particle Physics Proceedings''. ''Nuclear Physics B'' is part of the SCOAP3 initiative. Abstracting and indexing ''Nuclear Physics A'' * Current Contents ''Current Contents'' is a rapid alerting service database from Clarivate, formerly the Institute for Scientific Information and Thomson Reuters. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Differential Geometry
The ''Journal of Differential Geometry'' is a peer-reviewed scientific journal of mathematics published by International Press on behalf of Lehigh University in 3 volumes of 3 issues each per year. The journal publishes an annual supplement in book form called ''Surveys in Differential Geometry''. It covers differential geometry and related subjects such as differential equations, mathematical physics, algebraic geometry, and geometric topology. The editor-in-chief is Shing-Tung Yau of Harvard University. History The journal was established in 1967 by Chuan-Chih Hsiung, who was a professor in the Department of Mathematics at Lehigh University at the time. Hsiung served as the journal's editor-in-chief, and later co-editor-in-chief, until his death in 2009. In May 1996, the annual Geometry and Topology conference which was held at Harvard University was dedicated to commemorating the 30th anniversary of the journal and the 80th birthday of its founder. Similarly, in May 2008 Ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The American Mathematical Society
''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. The journal is devoted to shorter research articles. As a requirement, all articles must be at most 15 printed pages. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor of 0.813. Scope ''Proceedings of the American Mathematical Society'' publishes articles from all areas of pure and applied mathematics, including topology, geometry, analysis, algebra, number theory, combinatorics, logic, probability and statistics. Abstracting and indexing This journal is indexed in the following databases: 2011. American Mathematical Society. * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quaternionic Manifold
In differential geometry, a quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than the one for complex manifolds due in part to the noncommutativity of the quaternions and in part to the lack of a suitable calculus of holomorphic functions for quaternions. The most succinct definition uses the language of ''G''-structures on a manifold. Specifically, a quaternionic ''n-''manifold can be defined as a smooth manifold of real dimension 4''n'' equipped with a torsion-free \operatorname(n, \mathbb)\cdot\mathbb^\times-structure. More naïve, but straightforward, definitions lead to a dearth of examples, and exclude spaces like quaternionic projective space which should clearly be considered as quaternionic manifolds. Early history Marcel Berger's 1955 paper on the classification of Riemannian holonomy groups first raised the issue of the existence of non-symmetric manifolds with holonomy Sp(''n'')·Sp(1).Interestin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twistor Space
In mathematics and theoretical physics (especially twistor theory), twistor space is the complex vector space of solutions of the twistor equation \nabla_^\Omega_^=0 . It was described in the 1960s by Roger Penrose and Malcolm MacCallum. According to Andrew Hodges, twistor space is useful for conceptualizing the way photons travel through space, using four complex numbers. He also posits that twistor space may aid in understanding the asymmetry of the weak nuclear force. Informal motivation In the (translated) words of Jacques Hadamard: "the shortest path between two truths in the real domain passes through the complex domain." Therefore when studying four-dimensional space \mathbb^4 it might be valuable to identify it with \mathbb^2. However, since there is no canonical way of doing so, instead all isomorphisms respecting orientation and metric between the two are considered. It turns out that complex projective 3-space \mathbb^3 parametrizes such isomorphisms together with co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dmitry Kaledin
Dmitry (); Church Slavic form: Dimitry or Dimitri (); ancient Russian forms: D'mitriy or Dmitr ( or ) is a male given name common in Orthodox Christian culture, the Russian version of Demetrios (, ). The meaning of the name is "devoted to, dedicated to, or follower of Demeter" (Δημήτηρ, ''Dēmētēr''), "mother-earth", the Greek goddess of agriculture. Short forms of the name from the 13th–14th centuries are Mit, Mitya, Mityay, Mit'ka or Miten'ka (, or ); from the 20th century (originated from the Church Slavic form) are Dima, Dimka, Dimochka, Dimulya, Dimusha, Dimon etc. (, etc.) St. Dimitri's Day The feast of the martyr Saint Demetrius of Thessalonica is celebrated on Saturday before November 8 Old Style and New Style dates">Old Style: October 26]. The name day (именины): October 26 (November 8 on the Julian Calendar) See also: Eastern Orthodox liturgical calendar. The Saturday before this is called Demetrius Saturday and commemorates the Orthodox soldiers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
