共查询到20条相似文献,搜索用时 15 毫秒
1.
Zhuan Ye 《Inventiones Mathematicae》1995,122(1):475-507
Summary We first prove a theorem concerning higher order logarithmic partial derivatives for meromorphic functions of several complex variables. Then we show the best nature of the second main theorem in Nevanlinna theory under two different assumptions of non-degeneracy of meromorphic mappingsf :
n
n
for arbitrary positive integersn andm. Moreover, we derive a upper bound of the error term in the second main theorem for meromorphic mappings of finite order. Finally, we demonstrate the sharpness of all upper bounds in our main theorems.Oblatum 28-IX-1994 & 29-V-1995 相似文献
2.
Summary
This paper is devoted to make a systematic study of real hypersurfaces of quaternionic projective space using focal set theory. We obtain three types of such real hypersurfaces. Two of them are known. Third type is new and in its study the first example of proper quaternion CR-submanifold appears. We study real hypersurfaces with constant principal curvatures and classify such hypersurfaces with at most two distinct principal curvatures. Finally we study the Ricci tensor of a real hypersurface of quaternionic projective space and classify pseudo-Einstein, almost-Einstein and Einstein real hypersurfaces. 相似文献
3.
SHARIEF DESHMUKH 《Proceedings Mathematical Sciences》2011,121(2):171-179
In this paper, we classify real hypersurfaces in the complex projective space
C P\fracn+12C P^{\frac{n+1}{2}} whose structure vector field is a φ-analytic vector field (a notion similar to analytic vector fields on complex manifolds). We also define Jacobi-type vector
fields on a Riemannian manifold and classify real hypersurfaces whose structure vector field is a Jacobi-type vector field. 相似文献
4.
5.
6.
We prove the following Hartogs-Bochner type theorem: Let M be a connected C2 hypersurface of Pn(C) (n≥2) which divides Pn(C) in two connected open sets Ω1 and Ω2. Suppose that M has at most one open CR orbit. Then there exists i∈{1,2} such that C1 CR functions defined on M extends holomorphically to Ω
i
.
Supported by the TMR network. 相似文献
7.
8.
In this paper, we prove that the only compact two-sided hypersurfaces with constant mean curvature H which are weakly stable in
and have constant scalar curvature are (i) the twofold covering of a totally geodesic projective space; (ii) the geodesic spheres in
; and (iii) the quotient to
of the hypersurface
obtained as the product of two spheres of dimensions k and n − k, with k = 1,..., n − 1, and radii r and
, respectively, with
. 相似文献
9.
Mihai Păun 《Mathematische Annalen》2008,340(4):875-892
The results we obtain in this article concern the hyperbolicity of very generic hypersurfaces in the 3-dimensional projective
space: we show that the Kobayashi conjecture is true in this setting, as long as the degree of the hypersurface is greater
than 18. 相似文献
10.
11.
Let M
n
be a compact (two-sided) minimal hypersurface in a Riemannian manifold . It is a simple fact that if has positive Ricci curvature then M cannot be stable (i.e. its Jacobi operator L has index at least one). If is the unit sphere and L has index one, then it is known that M must be a totally geodesic equator.?We prove that if is the real projective space , obtained as a metric quotient of the unit sphere, and the Jacobi operator of M has index one, then M is either a totally geodesic sphere or the quotient to the projective space of the hypersurface obtained as the product of two spheres of dimensions n
1, n
2 and radius R
1, R
2, with and .
Received: June 6, 1998 相似文献
12.
The defect relation for holomorphic maps
in respect to slowly moving target hyperplanes in
is proved. The sharp defect boundn+1 is obtained.
Communicated by Yoram Sagher 相似文献
13.
D. D. Ilmuradov 《Ukrainian Mathematical Journal》1993,45(3):402-407
A thorough investigation of the characteristic of contingency of a second-category set in
m+1 is presented. In particular, the graph of a Lipschitz function is studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 378–383, March, 1993. 相似文献
14.
Tomokuni Takahashi 《Geometriae Dedicata》2011,154(1):183-206
We classify the certain type of relative quadric hypersurfaces of 3-dimensional projective space bundles over a projective
line or an elliptic curve whose fiber is the direct product of 2 projective lines. 相似文献
15.
Juan de Dios Prez Florentino G. Santos 《Differential Geometry and its Applications》2008,26(2):218-223
We classify real hypersurfaces of complex projective space , m3, with -recurrent structure Jacobi operator and apply this result to prove the non-existence of such hypersurfaces with recurrent structure Jacobi operator. 相似文献
16.
In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential operations are closed. On basis of these works, we firstly prove the Second Main Theorem concerning small algebroid functions for v-valued algebroid functions. 相似文献
17.
18.
We generalize the second pinching theorem for minimal hypersurfaces in a sphere due to Peng–Terng, Wei–Xu, Zhang, and Ding–Xin to the case of hypersurfaces with small constant mean curvature. Let $M^n$ be a compact hypersurface with constant mean curvature $H$ in $S^{n+1}$ . Denote by $S$ the squared norm of the second fundamental form of $M$ . We prove that there exist two positive constants $\gamma (n)$ and $\delta (n)$ depending only on $n$ such that if $|H|\le \gamma (n)$ and $\beta (n,H)\le S\le \beta (n,H)+\delta (n)$ , then $S\equiv \beta (n,H)$ and $M$ is one of the following cases: (i) $S^{k}\Big (\sqrt{\frac{k}{n}}\Big )\times S^{n-k}\Big (\sqrt{\frac{n-k}{n}}\Big )$ , $\,1\le k\le n-1$ ; (ii) $S^{1}\Big (\frac{1}{\sqrt{1+\mu ^2}}\Big )\times S^{n-1}\Big (\frac{\mu }{\sqrt{1+\mu ^2}}\Big )$ . Here $\beta (n,H)=n+\frac{n^3}{2(n-1)}H^2+\frac{n(n-2)}{2(n-1)} \sqrt{n^2H^4+4(n-1)H^2}$ and $\mu =\frac{n|H|+\sqrt{n^2H^2+ 4(n-1)}}{2}$ . 相似文献
19.
We classify certain real hypersurfaces of a quaternionic projective space satisfying some conditions on their Ricci tensors.Research partially supported by DGICYT Grant PS87-0115-C03-02 相似文献