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HIGHER DIMENSIONAL ANALOGUES OF CHÂTELET SURFACES
"... Abstract. We discuss the geometry and arithmetic of higherdimensional analogues of Châtelet surfaces; namely, we describe the structure of their Brauer and Picard groups and show that they can violate the Hasse principle. In addition, we use these varieties to give straightforward generalizations o ..."
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Abstract. We discuss the geometry and arithmetic of higherdimensional analogues of Châtelet surfaces; namely, we describe the structure of their Brauer and Picard groups and show that they can violate the Hasse principle. In addition, we use these varieties to give straightforward generalizations
Higherdimensional analogues of DonaldsonWitten theory
 Nucl. Phys. B
, 1997
"... We present a DonaldsonWitten type field theory in eight dimensions on manifolds with Spin(7) holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar ..."
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Cited by 42 (5 self)
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. This statement is a higher dimensional analogue of the fact that DonaldsonWitten field theory on hyperKähler 4manifolds is topological without twisting. Higher dimensional analogues of Floer cohomology are briefly outlined. All of these theories arise naturally within the context of string theory. 1
THE TWODIMENSIONAL ANALOGUE OF GENERAL RELATIVITY
, 1993
"... General Relativity in three or more dimensions can be obtained by taking the limit ω → ∞ in the BransDicke theory. In two dimensions General Relativity is an unacceptable theory. We show that the twodimensional closest analogue of General Relativity is a theory that also arises in the limit ω → ∞ ..."
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General Relativity in three or more dimensions can be obtained by taking the limit ω → ∞ in the BransDicke theory. In two dimensions General Relativity is an unacceptable theory. We show that the twodimensional closest analogue of General Relativity is a theory that also arises in the limit ω
A Two Dimensional Analogue of the Virasoro Algebra
, 2008
"... In this article, we study the cohomology of Lie algebras of vector fields of holomorphic type V ect1,0(M) on a complex manifold M. The main result is the introduction of a kind of order filtration on the continuous cochains on V ect1,0(M) and the calculation of the second term of the resulting spect ..."
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Cited by 1 (1 self)
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analogue of the Witt algebra. Then, we define, following Etingof and Frenkel, a central extension which is consequently a 2 dimensional analogue of the Virasoro algebra our cohomology calculations showing that it is a universal central extension.
Higherdimensional analogue of McVittie solution
 Grav. Cosmol
, 1990
"... A generalization of the McVittie solution, representing spacetime of a mass particle placed in (n + 2) dimensional RobertsonWalker universe is reported. ..."
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Cited by 2 (0 self)
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A generalization of the McVittie solution, representing spacetime of a mass particle placed in (n + 2) dimensional RobertsonWalker universe is reported.
There is no two dimensional analogue of Lamé’s equation
, 1992
"... The Lamé equation is the best known of a class of onedimensional, periodic Schrödinger equations for which all Bloch eigenvalues and multipliers can be explicitly parameterized by meromorphic functions defined on a compact Riemann surface. The purpose of this paper is to prove that there is no ..."
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Cited by 5 (0 self)
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The Lamé equation is the best known of a class of onedimensional, periodic Schrödinger equations for which all Bloch eigenvalues and multipliers can be explicitly parameterized by meromorphic functions defined on a compact Riemann surface. The purpose of this paper is to prove that there is no
On a three dimensional analogue to the holomorphic zpowers
, 2010
"... The main objective of this article is a constructive generalization of the holomorphic power and Laurent series expansions in C to dimension 3 using the framework of hypercomplex function theory. For this reason, deals the first part of this article with generalized Fourier & Taylor series exp ..."
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Cited by 4 (0 self)
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expansions in the space of square integrable quaternionvalued functions which possess peculiar properties regarding the hypercomplex derivative and primitive. In analogy to the complex onedimensional case, both series expansions are orthogonal series with respect to the unit ball in R3 and their series
1Platonic solids generate their fourdimensional analogues
"... In this paper, we show how regular convex 4polytopes – the analogues of the Platonic solids in four dimensions – can be constructed from threedimensional considerations concerning the Platonic solids alone. Via the CartanDieudonne ́ theorem, the reflective symmetries of the Platonic solids genera ..."
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In this paper, we show how regular convex 4polytopes – the analogues of the Platonic solids in four dimensions – can be constructed from threedimensional considerations concerning the Platonic solids alone. Via the CartanDieudonne ́ theorem, the reflective symmetries of the Platonic solids
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154,203