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103
Deformations Of Calibrated Submanifolds
 Commun. Analy. Geom
, 1996
"... . Assuming the ambient manifold is Kahler, the theory of complex submanifolds can be placed in the more general context of calibrated submanifolds, see [HL]. It is therefore natural to try to extend some of the many results in complex geometry to the other calibrated geometries of [HL]. In particula ..."
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. Assuming the ambient manifold is Kahler, the theory of complex submanifolds can be placed in the more general context of calibrated submanifolds, see [HL]. It is therefore natural to try to extend some of the many results in complex geometry to the other calibrated geometries of [HL]. In particular, the question of deformability of calibrated submanifolds is addressed here (analogous to Kodaira's work on deformations of complex submanifolds [K]). Also, a formula for the second variation of volume of an arbitrary calibrated submanifolds which generalizes a result of Simons' in the complex category [S] is given. 1. Introduction and summary General Remarks. In this paper, we discuss the deformation theory of calibrated submanifolds of Riemannian manifolds with restricted holonomy. Most of the definitions of the terms used in this introduction can be found in the seminal paper of Harvey and Lawson ([HL]). Throughout, we denote the ambient manifold by M and the submanifold by X. Recall ...
Heterotic flux compactifications and their moduli
, 2006
"... We study supersymmetric compactification to four dimensions with nonzero Hflux in heterotic string theory. The background metric is generically conformally balanced and can be conformally Kähler if the primitive part of the Hflux vanishes. Analyzing the linearized variational equations, we write ..."
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Cited by 21 (3 self)
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We study supersymmetric compactification to four dimensions with nonzero Hflux in heterotic string theory. The background metric is generically conformally balanced and can be conformally Kähler if the primitive part of the Hflux vanishes. Analyzing the linearized variational equations, we write down necessary conditions for the existence of moduli associated with the metric. In a heterotic model that is dual to a IIB compactification on an orientifold, we find the metric moduli in a fixed Hflux background via duality and check that they satisfy the required conditions. We also discuss expressing the conditions for moduli in a fixed flux background using twisted differential operators.
COHERENT STATE EMBEDDINGS, POLAR DIVISORS AND CAUCHY FORMULAS
, 1999
"... Abstract. For arbitrary quantizable compact Kähler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the sc ..."
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Cited by 19 (12 self)
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Abstract. For arbitrary quantizable compact Kähler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vectors on the manifold with the corresponding scalar products on projective space (Cauchy formulas), twopoint, threepoint and more generally cyclic mpoint functions are discussed. The threepoint function is related to the shape invariant of geodesic triangles in projective space. 1.
Transgression forms and extensions of ChernSimons gauge theories, JHEP 0601
, 2006
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Regulators and Characteristic Classes of Flat Bundles
"... In this paper, we prove that on any nonsingular algebraic variety, the characteristic classes of CheegerSimons and Beilinson agree whenever they can be interpreted as elements of the same group (e.g. for at bundles). In the universal case, where the base is BGL(C)^δ, we show that the uni ..."
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Cited by 16 (2 self)
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In this paper, we prove that on any nonsingular algebraic variety, the characteristic classes of CheegerSimons and Beilinson agree whenever they can be interpreted as elements of the same group (e.g. for at bundles). In the universal case, where the base is BGL(C)^&delta;, we show that the universal CheegerSimons class is half the Borel regulator element. We were unable to prove that the universal Beilinson class and the universal CheegerSimons classes agree in this universal case, but conjecture they do agree.
Invariant effective actions, cohomology of homogeneous spaces and anomalies
 Nucl. Phys. B
, 1995
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GRASSMANNIAN SPECTRAL SHOOTING
, 2010
"... We present a new numerical method for computing the purepoint spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting and matching approach, all the relevant information is carried by the flow projected onto the underlying Grassmann manifo ..."
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Cited by 10 (5 self)
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We present a new numerical method for computing the purepoint spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting and matching approach, all the relevant information is carried by the flow projected onto the underlying Grassmann manifold. We show how to numerically construct this projected flow in a stable and robust manner. In particular, the method avoids representation singularities by, in practice, choosing the best coordinate patch representation for the flow as it evolves. The method is analytic in the spectral parameter and of complexity bounded by the order of the spectral problem cubed. For large systems it represents a competitive method to those recently developed that are based on continuous orthogonalization. We demonstrate this by comparing the two methods in three applications: Boussinesq solitary waves, autocatalytic travelling waves and the Ekman boundary layer.