共查询到20条相似文献,搜索用时 10 毫秒
1.
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
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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
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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
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Atsushi Ikeda 《Mathematische Zeitschrift》2009,263(4):923-937
We investigate the subvarieties contained in generic hypersurfaces of projective toric varieties and prove two main theorems.
The first generalizes Clemens’ famous theorem on the genus of curves in hypersurfaces of projective spaces to curves in hypersurfaces
of toric varieties and the second improves the bound in the special case of toric varieties in a theorem of Ein on the positivity
of subvarieties contained in sufficiently ample generic hypersurfaces of projective varieties. Both depend on a hypothesis
which deals with the surjectivity of multiplication maps of sections of line bundles on the toric variety. We also obtain
an infinitesimal Torelli theorem for hypersurfaces of toric varieties. 相似文献
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Sadahiro Maeda 《Mathematische Annalen》1983,263(4):473-478
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M. G. Zaidenberg 《Functional Analysis and Its Applications》2009,43(2):113-118
We modify the deformation method in [16] to construct further examples of Kobayashi hyperbolic surfaces in \(\mathbb{P}_\mathbb{C}^3 \) of any even degree d ? 8. 相似文献
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Let M be a real hypersurface with almost contact metric structure ${(\phi, \xi, \eta, g)}$ in a complex projective space ${P_{n}\mathbb{C}}$ . A Real hypersurface M is said to be a Hopf hypersurface if ξ is principal. In this paper we investigate real hypersurfaces of ${P_{n}\mathbb{C}}$ whose Ricci tensors S satisfy ${\nabla_{\phi\nabla_{\xi}\xi}S = 0}$ . Under some further conditions we characterize Hopf hypersurfaces of ${P_{n}\mathbb{C}}$ . 相似文献
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We study compact minimal generic submanifolds of a complex projective space with flat normal connection and prove a reduction theorem of codimension under the condition on the Ricci tensor.The present studies were supported by the Basic Science Research Institute Program, Korea Ministry of Education, 1993-114. 相似文献
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Yusaku Tiba 《Mathematische Zeitschrift》2012,272(3-4):1165-1186
We deal with a holomorphic map from the complex plane ${\mathbb{C}}$ to the n-dimensional complex projective space ${\mathbb{P}^{n}(\mathbb{C})}$ and prove the Nevanlinna Second Main Theorem for some families of non-linear hypersurfaces in ${\mathbb{P}^{n}(\mathbb{C})}$ . This Second Main Theorem implies the defect relation. If the degree of the hypersurfaces are sufficiently large, the defect of the map is smaller than one. This means that holomorphic maps which omit the irreducible hypersurface of large degree is algebraically degenerate. To prove the Second Main Theorem, we use a meromorphic partial projective connection which is totally geodesic with respect to these hypersurfaces. A meromorphic partial projective connection is a family of locally defined meromorphic connections such which work as an entirely defined meromorphic connection under the Wronskian operator. By resolving the singularity and pulling back a meromorphic partial projective connection, we also prove the Second Main Theorem for singular hypersurfaces in ${\mathbb{P}^{n}(\mathbb{C})}$ , and prove the Second Main Theorem for smooth hypersurfaces in ${\mathbb{P}^{2}(\mathbb{C})}$ which are not normal crossing. 相似文献
16.
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
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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
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设Mn是复射影空间CPn+p/2中具有平坦法丛的一般极小子流形.该文研究了这种子流形的曲率性质与几何性质之间的关系.运用活动标架法,得到关于Ricci曲率和第二基本形式模长的刚性定理,完善了已有文献的相关结果.此外,该文还得到具有平坦法丛的一般子流形一个重要性质. 相似文献
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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
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Juan de Dios Pérez Florentino G. Santos 《Differential Geometry and its Applications》2005,22(2):181-188
We classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Lie parallel in the direction of the structure vector field. 相似文献