On cotangent manifolds, complex structures and generalized geometry
نویسندگان
چکیده
منابع مشابه
Almost Complex Structures on the Cotangent Bundle
We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This unifies the complete lift defined by I.Satô and the horizontal lift introduced by S.Ishihara and K.Yano. We study some geometric properties of this lift and its compatibility with symplectic forms on the cotangent bundle.
متن کاملLectures on complex geometry, Calabi–Yau manifolds and toric geometry
These are introductory lecture notes on complex geometry, Calabi–Yau manifolds and toric geometry. We first define basic concepts of complex and Kähler geometry. We then proceed with an analysis of various definitions of Calabi–Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi–Yau manifolds in two different ways; as hypersurfaces in to...
متن کاملOn some generalized recurrent manifolds
The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds, called, super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [A.A. Shaikh and A. Patra, On a generalized class of recurrent manifolds, Arch. Math. (Brno) 46 (2010) 71--78.] and weakly generalized recurrent manifolds ...
متن کاملFano Manifolds, Contact Structures, and Quaternionic Geometry
Let Z be a compact complex (2n+1)-manifold which carries a complex contact structure, meaning a codimension-1 holomorphic sub-bundle D ⊂ TZ which is maximally non-integrable. If Z admits a Kähler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kähler manifold (M, g). If Z also admits a second complex contact structure D̃ 6= D, then Z = C...
متن کاملGeneralized complex geometry
Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and study generalized complex branes, which interpolate between flat bundles on Lagrangian submanifold...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2016
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.3003