Functions Holomorphic along Holomorphic Vector Fields
نویسندگان
چکیده
منابع مشابه
Holomorphic vector-valued functions
exists. The function f is continuously differentiable when it is differentiable and f ′ is continuous. A k-times continuously differentiable function is C, and a continuous function is C. A V -valued function f is weakly C when for every λ ∈ V ∗ the scalar-valued function λ◦ f is C. This sense of weak differentiability of a function f does not refer to distributional derivatives, but to differe...
متن کاملHolomorphic vector fields and minimal Lagrangian submanifolds
The purpose of this note is to establish the following theorem: Let N be a Kahler manifold, L be an oriented immersed minimal Lagrangian submanifold of N without boundary and V be a holomorphic vector field in a neighbourhood of L in N . Let div(V ) be the (complex) divergence of V . Then the integral ∫ L div(V ) = 0. Vice versa suppose that N is Kahler-Einstein with non-zero scalar curvature a...
متن کاملFrom Holomorphic Functions to Holomorphic Sections
It is a pleasure to have the opportunity in the graduate colloquium to introduce my research field. I am a differential geometer. To be more precise, I am a complex differential geometer, although I am equally interested in real differential geometry. To many people, geometry is a kind of mathematics that is related to length, area, volume, etc. For the Euclidean geometry, this is indeed the ca...
متن کاملMonotonicity and holomorphic functions
This is a survey on some recent works, mainly by the author on the relation between holomorphic functions on Kähler manifolds, monotonicity and the geometry of complex manifolds. We also use this opportunity to give details of a sketched step in the proof of a previously established result. Math Subject Classifications. Primary: 58G11, 53C44.
متن کاملSome Remarks on Indices of Holomorphic Vector Fields
One can associate several residue-type indices to a singular point of a two-dimensional holomorphic vector field. Some of these indices depend also on the choice of a separatrix at the singular point. We establish some relations between them, especially when the singular point is a generalized curve and the separatrix is the maximal one. These local results have global consequences, for example...
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: Journal of Geometric Analysis
سال: 2009
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-009-9078-7