Locally Conformal Kähler Geometry

Dragomir, Sorin; Орнеа, Ливиу

doi:10.1007/978-1-4612-2026-8

Cited by 261 publications

(259 citation statements)

References 0 publications

Supporting

Mentioning

255

Contrasting

Unclassified

Order By: Relevance

“…-Let z 1 , ..., z m be the standard complex coordinate func- ρ : π 1 (S M ) → R >0 and a closed strongly positive (1, 1)-form ω on the universal cover of S M such that g * ω = ρ(g)ω for all g ∈ π 1 (S M ); cf. [2]. We now investigate the existence of locally conformally Kähler metrics more generally on the manifolds X(K, U ).…”

Section: Take Now a Holomorphic Functionmentioning

confidence: 99%

Non-Kähler compact complex manifolds associated to number fields

Oeljeklaus

Toma

2005

Annales De L’institut Fourier

107

210

View full text Add to dashboard Cite

Section: Take Now a Holomorphic Functionmentioning

confidence: 99%

Non-Kähler compact complex manifolds associated to number fields

Oeljeklaus

Toma

2005

Annales De L’institut Fourier

107

210

View full text Add to dashboard Cite

“…The reader can consult the book [9] for more examples. Hence the conformal class of Ω is a lcs structure on M , we denote S(α).…”

Section: Examplesmentioning

confidence: 99%

Some properties of locally conformal symplectic structures

Banyaga¹

2002

Comment. Math. Helv.

View full text Add to dashboard Cite

Abstract. We show that the dω-cohomology is isomorphic to a conformally invariant usual de Rham cohomology of an appropriate cover. We also prove a Moser theorem for locally conformal symplectic (lcs) forms. We point out a connection between lcs geometry and contact geometry. Finally, we show the connections between first kind, second kind, essential, inessential, local, and global conformal symplectic structures through several invariants. Mathematics Subject Classification (2000). 53C12; 53C15.Keywords. Locally conformal symplectic structures, Lee form, extended Lee homomorphism, de Rham invariant, Gelfand-Fucks invariant, Lee invariant, conformal invariants, essential/inessential conformal structures, the dω cohomology, the cA-cohomology. PreliminariesA locally conformal symplectic (lcs) form on a smooth manifold M is a nondegenerate 2-form Ω such that there exists an open cover U = (U i ) and smooth positive functions λ i on U i such thatis a symplectic form on U i . If for all i, λ i = 1, the form Ω is a symplectic form. Lee [15] observed that the 1-forms {d(ln λ i )} fit together into a closed 1-form ω such that dΩ = −ω ∧ Ω. Two lcs forms Ω, Ω on a smooth manifold M are said to be (conformally) equivalent if Ω = f Ω, for some positive function f on M .A locally conformal symplectic (lcs) structure S on a smooth manifold M is an equivalence class of lcs forms.

show abstract

“…If the foliation T is regular, as it happens for the solution Sol = CH 4 α , g 8 , ω, Ω, ϕ that we found in section 5.1, then the following result holds [49,53]. • The leaves are totally geodesic flat torii.…”

Section: Foliations and Principal Torus Fibrations On Vaisman Manifoldsmentioning

confidence: 64%

“…This Spin(7)-structure induces a G 2 -structure on the leafs of the canonical foliation F. If we restrict to the class of Hopf manifolds inside the class of Vaisman manifolds, then we have a very explicit result about the G 2 -structure present in the leaves. Notice that the solution of section 5.1 is a Hopf manifold, so the following result applies [49,53].…”

Section: Jhep09(2015)178mentioning

confidence: 95%

“…Notice that the Hopf manifold that we found in section 5.1 to satisfy the local equations of motion of eleven-dimensional Supergravity is a particular example of Hopf manifold. A Vaisman manifold (M, ω) is equipped with four canonical foliations, which are defined on (M, ω) by means of the Lee-form θ and the complex structure J of M as follows [49,53]:…”

Section: Foliations and Principal Torus Fibrations On Vaisman Manifoldsmentioning

confidence: 99%

See 1 more Smart Citation

M-theory on non-Kähler eight-manifolds

Shahbazi

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

Abstract:We show that M-theory admits a class of supersymmetric eight-dimensional compactification background solutions, equipped with an internal complex pure spinor, more general than the Calabi-Yau one. Building-up on this result, we obtain a a particular class of supersymmetric M-theory eight-dimensional non-geometric compactification backgrounds with external three-dimensional Minkowski space-time, proving that the global space of the non-geometric compactification is again a differentiable manifold, although with very different geometric and topological properties respect to the corresponding standard M-theory compactification background: it is a compact complex manifold admitting a Kähler covering with deck transformations acting by holomorphic homotheties with respect to the Kähler metric. We show that this class of non-geometric compactifications evade the Maldacena-Nuñez no-go theorem by means of a mechanism originally developed by Mario García-Fernández and the author for Heterotic Supergravity, and thus do not require l P -corrections to allow for a nontrivial warp factor or four-form flux. We obtain an explicit compactification background on a complex Hopf four-fold that solves all the equations of motion of the theory, including the warp factor equation of motion. We also show that this class of non-geometric compactifications are equipped with a holomorphic principal torus fibration over a projective Kähler base as well as a codimension-one foliation with nearly-parallel G 2 -leaves, making thus contact with the work of M. Babalic and C. Lazaroiu on the foliation structure of the most general M-theory supersymmetric compactifications.

show abstract

Locally Conformal Kähler Geometry

Cited by 261 publications

References 0 publications

Non-Kähler compact complex manifolds associated to number fields

Non-Kähler compact complex manifolds associated to number fields

Some properties of locally conformal symplectic structures

M-theory on non-Kähler eight-manifolds

Contact Info

Product

Resources

About