Generalized Complex Geometry
By M. Gualtieri. University Lecture Series, 2004
1,579 citations recorded by the source corpus.
Generalized complex geometry encompasses complex and symplectic ge- ometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deforma- tion theory, relation to Poisson geometry, and local structure theory. We also dene and study generalized complex branes, which interpolate be- tween at bundles on Lagrangian submanifolds and holomorphic bundles on complex submanifolds.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/00ffdbdc44d47a998adfe2547a88d0bb8e48d975
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Citations in the corpus
- Supersymmetric backgrounds from generalized Calabi‐Yau manifolds (2004, background): “1In [8], the same name is used for a different type of manifold, that has two pure spinors whose associated generalized complex structures are commuting and integrable.”
- The decomposition of forms and cohomology of generalized complex manifolds (2006, neutral): “The space U can also be seen as the ik-eigenspace of the Lie algebra action of J (see [6]).”
- Generalized structures of N=1 vacua (2005, neutral): “Keywords: Differential and Algebraic Geometry, Supergravity Models, Superstring Vacua. c© SISSA 2005 http://jhep.sissa.it/archive/papers/jhep112005020/jhep112005020.pdf J H E P 1 1 ( 2 0 0 5 ) 0 2 0 Contents”
- Bihermitian metrics on Del Pezzo surfaces (2006, methodology): “th respect to both. When M is compact with even first Betti number, and ω+,ω− are the two hermitian forms, the authors show that dc − ω − = H = −dc + ω + for a closed 3-form H which is equivalent (see [4]) to the definition in the introduction. Given a bihermitian metric, the fundamental object to stu”
- Generalized geometry and the Hodge decomposition (2004, background): “As defined in [3], it consists of two commuting generalized complex structures (J1,J2) such that the involution −J1J2 = G determines a generalized Riemannian metric on T ⊕ T .”
- The Gauge algebra of double field theory and Courant brackets (2009, background): “11)) of sections P,Q,R of T ⊕ T ∗ is given by [9, 8]: J(P,Q,R) = dN(P,Q,R), (7.”
- Maximally homogeneous para-CR manifolds of semisimple type (2006, neutral): “2 This structure is related to how the map is derived in chapter 6 of [ 1 ]”
- Poisson geometry and Morita equivalence (2004, background): “is a real 2-form, and Lis a generalized complex structure on P(see Remark 2.11), then one can show that τB(L) is again a generalized complex structure, and this operation is called a B-field transform [42, 45]. If Π is a Poisson structure on P, then changing it by a gauge transformation will generall”
- Lectures on generalized geometry (2010, background): “ warned that different authors have different conventions (or occasionally this author too!). For other accounts of generalized geometry, I should direct the reader to the papers and surveys (e.g. [2], [8]) of my former students Marco Gualtieri and Gil Cavalcanti who have developed many aspects of the”
- Electric-Magnetic Duality And The Geometric Langlands Program (2006, background): “3 of [67], J = 1 2 ( J+ + J− −(ω−1 + − ω−1 − ) ω+ − ω− −(J t + + J t −) ) .”
- A correction to “Tamed symplectic forms and strong Kähler with torsion metrics” (2012, background): “SKT metrics have a central role in type II string theory, in two-dimensional supersymmetric σ-models (see [17, 40]) and they also have relations with generalized Kähler geometry (see for instance [1, 5, 14, 17, 22, 26]).”
- T-duality, generalized geometry and non-geometric backgrounds (2008, background): “This combination of V and X is actually none other than the Dorfman bracket [18,24] whose antisymmetrization gives the Courant bracket (2.”