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Найдена 71 публикация
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Статья
Losev A. S., Slizovskiy S. Journal of Geometry and Physics. 2011. Vol. 61. P. 1868-1880.
Добавлено: 27 февраля 2013
Статья
Marshakov A., Миронов А. Д., Морозов А. Ю. Journal of Geometry and Physics. 2011. Vol. 61. P. 1203-1222.
Добавлено: 28 февраля 2013
Статья
Akhmet’ev P. Journal of Geometry and Physics. 2013. Vol. 74. No. 213. P. 381-391.
Добавлено: 15 марта 2015
Статья
Buryak A., Posthuma H., Shadrin S. Journal of Geometry and Physics. 2012. Vol. 62. No. 7. P. 1639-1651.
Добавлено: 30 сентября 2020
Статья
Amerik, E., Campana, F. Journal of Geometry and Physics. 2013. Vol. 71. No. September. P. 53-57.

This is a note on Beauville's problem (solved by Greb, Lehn, and Rollenske in the non-algebraic case, and by Hwang and Weiss in general) whether a lagrangian torus on an irreducible holomorphic symplectic manifold is a fiber of a lagrangian fibration. We provide a different very short solution in the non-algebraic case, and make some observations suggesting a different approach in the algebraic case. © 2013 Elsevier B.V.

Добавлено: 26 мая 2013
Статья
E. Yakovlev, Lerman L. Journal of Geometry and Physics. 2019. Vol. 135. P. 70-79.
Добавлено: 22 октября 2018
Статья
Basalaev A. Journal of Geometry and Physics. 2018. Vol. 2014. No. 84. P. 73-86.
Добавлено: 26 февраля 2019
Статья
Basalaev A. Journal of Geometry and Physics. 2014. Vol. 77. P. 30-42.
Добавлено: 26 февраля 2019
Статья
Ionov A. Journal of Geometry and Physics. 2019. Vol. 140. P. 125-130.
Добавлено: 8 ноября 2019
Статья
Gurevich D., Saponov P. A. Journal of Geometry and Physics. 2016. Vol. 106. P. 87-97.

In our previous publications we introduced differential calculus on the enveloping algebras U(gl(m)) similar to the usual calculus on the commutative algebra . The main ingredients of our calculus are quantum partial derivatives which turn into the usual partial derivatives in the classical limit. In the particular case m=2 we prolonged this calculus on a central extension A of the algebra U(gl(2)). In the present paper we consider the problem of a further extension of the quantum partial derivatives on the skew-field of the algebra A and define the corresponding de Rham complex. As an application of the differential calculus we suggest a method of transferring dynamical models defined on an extended  to an extended algebra U(u(2)). We call this procedure the quantization with noncommutative configuration space. In this sense we quantize the Dirac monopole and find a solution of this model.

 

 

Добавлено: 4 мая 2016
Статья
Nirov Khazret S., Razumov A. V. Journal of Geometry and Physics. 2017. Vol. 112. P. 1-28.
Добавлено: 29 января 2018
Статья
Ogievetsky O., Pyatov P. N. Journal of Geometry and Physics. 2021. Vol. 162.
Добавлено: 27 декабря 2020
Статья
Aleksei Ivanov, Tikhomirov A. S. Journal of Geometry and Physics. 2018. Vol. 129. P. 90-98.
Добавлено: 25 февраля 2018
Статья
Covolo T., Grabowski J., Poncin N. Journal of Geometry and Physics. 2016. Vol. 110. P. 393-401.

Smooth -supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the ‘scalar product’ of the involved -degrees. It exhibits interesting changes in comparison with the sign rule using the parity of the total degree. With the new rule, nonzero degree even coordinates are not nilpotent, and even (resp., odd) coordinates do not necessarily commute (resp., anticommute) pairwise. The classical Batchelor–Gawȩdzki theorem says that any smooth supermanifold is diffeomorphic to the ‘superization’ ΠE of a vector bundle E. It is also known that this result fails in the complex analytic category. Hence, it is natural to ask whether an analogous statement goes through in the category of -supermanifolds with its local model made of formal power series. We give a positive answer to this question.

Добавлено: 12 ноября 2016
Статья
Izosimov A. Journal of Geometry and Physics. 2012. Vol. 62. No. 12. P. 2414-2423.
Добавлено: 18 ноября 2013
Статья
Soldatenkov A. O., Verbitsky M. Journal of Geometry and Physics. 2012. Vol. 62. No. 11. P. 2234-2240.

A hypercomplex manifold M is a manifold with a triple I,J,K of complex structure operators satisfying quaternionic relations. For each quaternion L=aI+bJ+cK, L2=−1, L is also a complex structure operator on M, called an induced complex structure. We study compact complex subvarieties of (M,L), for L a generic induced complex structure. Under additional assumptions (Obata holonomy contained in SL(n,H), the existence of an HKT-metric), we prove that (M,L) contains no divisors, and all complex subvarieties of codimension 2 are trianalytic (that is, also hypercomplex).

Добавлено: 30 августа 2012
Статья
Amerik E., Verbitsky M. Journal of Geometry and Physics. 2015. Vol. 97. P. 44-50.

Let S be an infinite-dimensional manifold of all symplectic, or hyperkähler, structures on a compact manifold M, and Diff0 the connected component of its diffeomorphism group. The quotient S/Diff0 is called the Teichmüller space of symplectic (or hyperkähler) structures on M. MBM classes on a hyperkähler manifold M are cohomology classes which can be represented by a minimal rational curve on a deformation of M. We determine the Teichmüller space of hyperkähler structures on a hyperkähler manifold, identifying any of its connected components with an open subset of the Grassmannian variety SO(b2-3, 3)/SO(3)×SO(b2-3) consisting of all Beauville-Bogomolov positive 3-planes in H2(M,R) which are not orthogonal to any of the MBM classes. This is used to determine the Teichmüller space of symplectic structures of Kähler type on a hyperkähler manifold of maximal holonomy. We show that any connected component of this space is naturally identified with the space of cohomology classes v∈H2(M,R) with q(v,v)>0, where q is the Bogomolov-Beauville-Fujiki form on H2(M,R). © 2015 Elsevier B.V.

Добавлено: 8 сентября 2015
Статья
Adler D., Gritsenko V. Journal of Geometry and Physics. 2020. Vol. 150. P. 103616.
Добавлено: 1 ноября 2019
Статья
Marshall I. Journal of Geometry and Physics. 2021. Vol. 170.
Добавлено: 6 октября 2021
Статья
Bobrova I., Mazzocco M. Journal of Geometry and Physics. 2021. Vol. 166.
Добавлено: 25 сентября 2021
Статья
Kharchev S., Zabrodin A. Journal of Geometry and Physics. 2015. Vol. 94. P. 19-31.
Добавлено: 12 октября 2015