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1.
Misha Verbitsky 《Mathematische Zeitschrift》2010,264(4):939-957
Let (M, ω) be a Kähler manifold. An integrable function ${\varphi}Let (M, ω) be a K?hler manifold. An integrable function j{\varphi} on M is called ω
q
-plurisubharmonic if the current ddcjùwq-1{dd^c\varphi\wedge \omega^{q-1}} is positive. We prove that j{\varphi} is ω
q
-plurisubharmonic if and only if j{\varphi} is subharmonic on all q-dimensional complex subvarieties. We prove that a ω
q
-plurisubharmonic function is q-convex, and admits a local approximation by smooth, ω
q
-plurisubharmonic functions. For any closed subvariety Z ì M{Z\subset M} ,
dim\mathbbC Z £ q-1{\dim_\mathbb{C} Z\leq q-1} , there exists a strictly ω
q
-plurisubharmonic function in a neighbourhood of Z (this result is known for q-convex functions). This theorem is used to give a new proof of Sibony’s lemma on integrability of positive closed (p, p)-forms which are integrable outside of a complex subvariety of codimension ≥ p + 1. 相似文献
2.
A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the three structures, and such that the corresponding Hermitian forms are closed, the manifold is said to be hyperkähler. In the paper “Non-Hermitian Yang–Mills connections” [13], Kaledin and Verbitsky proved that the twistor space of a hyperkähler manifold admits a balanced metric; these were first studied in the article “On the existence of special metrics in complex geometry” [17] by Michelsohn. In the present article, we review the proof of this result and then generalize it and show that twistor spaces of general compact hypercomplex manifolds are balanced. 相似文献
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4.
Francesco Catoni Roberto Cannata Enrico Nichelatti Paolo Zampetti 《Advances in Applied Clifford Algebras》2005,15(2):183-212
Systems of hypercomplex numbers, which had been studied and developed at the end of the 19th century, are nowadays quite unknown to the scientific community. It is believed that study of their applications ended just
before one of the fundamental discoveries of the 20th century, Einstein’s equivalence between space and time. Owing to this equivalence, not-defined quadratic forms have got concrete
physical meaning and have been recently recognized to be in strong relationship with a system of bidimensional hypercomplex
numbers. These numbers (called hyperbolic) can be considered as the most suitable mathematic language for describing the bidimensional space-time, in spite of some
unfamiliar algebraic properties common to all the commutative hypercomplex systems with more than two dimensions: they are
decomposable systems and there are non-zero numbers whose product is zero. With respect to the famous Hamilton quaternions,
one can introduce the differential calculus for the hyperbolic numbers and for all the commutative hypercomplex systems; moreover,
one can even introduce functions of hypercomplex variable.
The aim of this work is to study the systems of commutative hypercomplex numbers and the functions of hypercomplex variable
by describing them in terms of a familiar mathematical tool, i.e. matrix algebra. 相似文献
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7.
Mohamed El Kadiri 《Journal of Mathematical Analysis and Applications》2011,381(2):706-723
A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly plurifinely plurisubharmonic if and only if it is locally bounded from above in the plurifine topology and f°h is finely subharmonic for all complex affine-linear maps h. As a consequence, the regularization in the plurifine topology of a pointwise supremum of such functions is weakly plurifinely plurisubharmonic, and it differs from the pointwise supremum at most on a pluripolar set. Weak plurifine plurisubharmonicity and weak plurifine holomorphy are preserved under composition with weakly plurifinely holomorphic maps. 相似文献
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9.
O. I. Bogoyavlenskii 《Mathematical Notes》1970,8(1):514-517
It is proved that the property of a manifold Mn possessing a smooth function with given numbers of critical points of each index is homotopic invariant if Wh(
1 (Mn)) = 0 and every Z(
1 (Mn))-stable free module is free.Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 77–83, July, 1970. 相似文献
10.
We show that the LiouvilleD
p
-property is invariant under rough isometries between a Riemannian manifold of bounded geometry and a graph of bounded degree.
The first author was supported partly by the EU HCM contract No. CHRX-CT92-0071.
This article was processed by the author using the Springer-Verlag TEX P Jourlg macro package 1991. 相似文献
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12.
Almost hypercomplex pseudo-Hermitian manifolds are considered. Isotropic hyper-K?hler manifolds are introduced. A 4-parametric
family of 4-dimensional manifolds of this type is constructed on a Lie group. This family is characterized geometrically.
The condition a 4-manifold to be isotropic hyper-K?hler is given.
相似文献
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15.
Subharmonic functions on real and complex manifolds 总被引:7,自引:0,他引:7
Leon Karp 《Mathematische Zeitschrift》1982,179(4):535-554
16.
I. M. Gel'fand A. V. Zelevinskii M. M. Kapranov 《Functional Analysis and Its Applications》1989,23(2):94-106
M. V. Lomonosov Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 23, No. 2, pp. 12–26, April–June, 1989. 相似文献
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Shing-Tung Yau 《纯数学与应用数学通讯》1975,28(2):201-228