scholarly journals Conjugate connections with respect to a quadratic endomorphism and duality

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2367-2374 ◽  
Author(s):  
Cornelia-Livia Bejan ◽  
Mircea Crasmareanu
Keyword(s):  
Complex Geometry ◽  
Linear Connection ◽  
Main Interest ◽  
Conjugate Connections ◽  
Almost Complex ◽  
Conjugate Connection ◽  
Exponential Case

The goal of this paper is to consider the notion of conjugate connection in a unifying setting for both almost complex and almost product geometries, having as model the works of Mileva Prvanovic. A main interest is in finding classes of conjugate connections in duality with the initial linear connection; for example in the exponential case of almost complex geometry we arrive at a rule of quantization.

Mini-Workshop: Almost Complex Geometry

2021 ◽  
Vol 17 (4) ◽  
pp. 1657-1691
Author(s):  
Daniele Angella ◽  
Joana Cirici ◽  
Jean-Pierre Demailly ◽  
Scott Wilson
Keyword(s):  
Complex Geometry ◽  
Almost Complex

Lelong–Poincaré formula in symplectic and almost complex geometry

2020 ◽  
Vol 38 (3) ◽  
pp. 337-364
Author(s):  
Emmanuel Mazzilli ◽  
Alexandre Sukhov
Keyword(s):  
Complex Geometry ◽  
Almost Complex ◽  
Poincaré Formula

XXII.—Tensor Fields and Connections on Cross-Sections in the tangent bundle of a differentiable manifold

1967 ◽  
Vol 67 (4) ◽  
pp. 277-288
Author(s):  
Kentaro Yano
Keyword(s):  
Vector Field ◽  
Cross Section ◽  
Tangent Bundle ◽  
Complex Structure ◽  
Linear Connection ◽  
Differentiable Manifold ◽  
Tensor Fields ◽  
Linear Connections ◽  
Almost Complex ◽  
The Cross

SynopsisTensor fields and linear connections in an n-dimensional differentiable manifold M can be extended, in a natural way, to the tangent bundle T(M) of M to give tensor fields of the same type and linear connections in T(M) respectively. We call such extensions complete lifts to T(M) of tensor fields and linear connections in M.On the other hand, when a vector field V is given in M, V determines a cross-section which is an n-dimensional submanifold in the 2n-dimensional tangent bundle T(M).We study first the behaviour of complete lifts of tensor fields on such a cross-section. The complete lift of an almost complex structure being again an almost complex structure, we study especially properties of the cross-section as a submanifold in an almost complex manifold.We also study properties of cross-sections with respect to the linear connection which is the complete lift of a linear connection in M and with respect to the linear connection induced by the latter on the cross-section. To quote a typical result: A necessary and sufficient condition for a cross-section to be totally geodesic is that the vector field V in M defining the cross-section in T(M) be an affine Killing vector field in M.

scholarly journals GENERALIZED COMPLEX GEOMETRY AND THE POISSON SIGMA MODEL

2005 ◽  
Vol 20 (13) ◽  
pp. 985-995 ◽  
Author(s):  
L. BERGAMIN
Keyword(s):  
Sigma Model ◽  
Complex Geometry ◽  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Poisson Structures ◽  
Generalized Complex Structures ◽  
Almost Complex ◽  
Generalized Complex ◽  
Poisson Sigma Model

The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N = (2, 1) or N = (2, 2) supersymmetry, but a certain relation among the different Poisson structures is needed. Moreover, important relations of an additional almost complex structure are found, which have no immediate interpretation in terms of generalized complex structures.

scholarly journals Castelnuovo's bound and rigidity in almost complex geometry

2021 ◽  
Vol 379 ◽  
pp. 107550
Author(s):  
Aleksander Doan ◽  
Thomas Walpuski
Keyword(s):  
Complex Geometry ◽  
Almost Complex

scholarly journals A CONNECTION WITH PARALLEL TOTALLY SKEW-SYMMETRIC TORSION ON A CLASS OF ALMOST HYPERCOMPLEX MANIFOLDS WITH HERMITIAN AND ANTI-HERMITIAN METRICS

2011 ◽  
Vol 08 (01) ◽  
pp. 115-131 ◽  
Author(s):  
MANCHO MANEV ◽  
KOSTADIN GRIBACHEV
Keyword(s):  
Special Interest ◽  
Complex Structure ◽  
Linear Connection ◽  
Almost Complex Structure ◽  
Hermitian Metrics ◽  
Almost Complex ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds ◽  
The Subject ◽  
Norden Metrics

The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its torsion is totally skew-symmetric. The class of the nearly Kähler manifolds with respect to the first almost complex structure is of special interest. It is proved that D has a D-parallel torsion and is weak if it is not flat. Some curvature properties of these manifolds are studied.

Twist, elementary deformation and K/K correspondence in generalized geometry

2020 ◽  
Vol 31 (10) ◽  
pp. 2050078
Author(s):  
Vicente Cortés ◽  
Liana David
Keyword(s):  
Complex Geometry ◽  
Killing Vector ◽  
Kähler Manifold ◽  
Conformal Change ◽  
Kahler Manifold ◽  
Hirzebruch Surfaces ◽  
Almost Complex ◽  
Generalized Geometry ◽  
Twist Construction ◽  
Hermitian Structures

We define the conformal change and elementary deformation in generalized complex geometry. We apply Swann’s twist construction to generalized (almost) complex and Hermitian structures obtained by these operations and establish conditions for the Courant integrability of the resulting twisted structures. We associate to any appropriate generalized Kähler manifold [Formula: see text] with a Hamiltonian Killing vector field a new generalized Kähler manifold, depending on the choice of a pair of non-vanishing functions and compatible twist data. We study this construction when [Formula: see text] is toric, with emphasis on the four-dimensional case, and we apply it to deformations of the standard flat Kähler metric on [Formula: see text], the Fubini–Study metric on [Formula: see text] and the admissible Kähler metrics on Hirzebruch surfaces. As a further application, we recover the K/K (Kähler/Kähler) correspondence, by specializing to ordinary Kähler manifolds.

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