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1.
2.
We give a complete classification of -invariant real hypersurfaces in complex two-plane Grassmannians G
2(C
m+2) with commuting normal Jacobi operator .
The first author was supported by MCYT-FEDER grant BFM 2001-2871-C04-01, the second author by grant Proj. No. KRF-2006-351-C00004
from Korea Research Foundation and the third author by grant Proj. No. R14-2002-003-01001-0 from Korea Research Foundation,
Korea 2006 and Proj. No. R17-2007-006-01000-0 from KOSEF. 相似文献
3.
《Mathematische Nachrichten》2017,290(2-3):442-451
First we introduce the notion of parallel normal Jacobi operator for real hypersurfaces in the complex quadric . Next we give a complete classification of real hypersurfaces in the complex quadric with parallel normal Jacobi operator. 相似文献
4.
Young Jin Suh 《Mathematische Nachrichten》2019,292(6):1375-1391
First we introduce the notion of structure Jacobi operator of Codazzi type for real hypersurfaces in the complex quadric . Next we give a complete classification of real hypersurfaces in with structure Jacobi operator of Codazzi type. 相似文献
5.
Hyunjin Lee Juan de Dios Pérez Young Jin Suh 《Czechoslovak Mathematical Journal》2010,60(4):1025-1036
We introduce the new notion of pseudo-$
\mathbb{D}
$
\mathbb{D}
-parallel real hypersurfaces in a complex projective space as real hypersurfaces satisfying a condition about the covariant
derivative of the structure Jacobi operator in any direction of the maximal holomorphic distribution. This condition generalizes
parallelness of the structure Jacobi operator. We classify this type of real hypersurfaces. 相似文献
6.
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
7.
We give some non-existence theorems for Hopf real hypersurfaces in complex two-plane Grassmannians G 2(? m+2) with parallel structure Jacobi operator R ξ. 相似文献
8.
In this paper we classify the real hypersurfaces in a non-flat complex space form with its structure Jacobi operator R ξ satisfying (? X R ξ )ξ = 0, for all vector fields X in the maximal holomorphic distribution D. With this result, we prove the non-existence of real hypersurfaces with D-parallel as well as D-recurrent structure Jacobi operator in complex projective and hyperbolic spaces. We can also prove the non-existence of real hypersurfaces with recurrent structure Jacobi operator in a non-flat complex space form as a corollary. 相似文献
9.
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
10.
We prove that the largest first eigenvalue of the Dirac operator among all Hermitian metrics on the complex projective space of odd dimension m, larger than the Fubini-Study metric is bounded by (2m(m+1))1/2.
Mathematics Subject Classification (2000): 53C27, 58J50, 58J60. 相似文献
11.
Lu Qikeng 《数学学报(英文版)》1998,14(1):1-8
In the complexn-dimensional projective spaceCP
n
, let λ
p
(=4p(p+n)) be the eigen value of the Laplace-Beltrami operator andH
p
be the space of all eigen functions of eigen value λ
p
. The reproducing kernelh
p
(z, w) ofH
p
is constructed explicitly in this paper, and a system of complete orthogohal functions ofH
p
is constructed fromh
p
(z,w)(p=1,2, …).
Partially supported by NSF of China 相似文献
12.
13.
Hyun Jin Lee Juan de Dios Pérez Florentino G. Santos Young Jin Suh 《Monatshefte für Mathematik》2009,60(4):187-194
We prove the non-existence of a certain family of real hypersurfaces in complex projective space. From this result we classify
real hypersurfaces whose structure Jacobi operator satisfies a condition that generalizes parallelness. 相似文献
14.
We give a non-existence theorem for Hopf hypersurfaces in complex two-plane Grassmannians G 2(? m+2) whose structure Jacobi operator R ξ is of Codazzi type. 相似文献
15.
Qing-Ming Cheng 《Proceedings of the American Mathematical Society》2008,136(9):3309-3318
Let be an -dimensional compact hypersurface with constant scalar curvature , , in a unit sphere . We know that such hypersurfaces can be characterized as critical points for a variational problem of the integral of the mean curvature . In this paper, we first study the eigenvalue of the Jacobi operator of . We derive an optimal upper bound for the first eigenvalue of , and this bound is attained if and only if is a totally umbilical and non-totally geodesic hypersurface or is a Riemannian product , .
16.
17.
In this paper we determine the real hypersurfaces for which the structure Jacobi operator commutes over both the Ricci tensors
and structure tensors (for a definition of the operator see Sect. 1). We prove that such hypersurfaces are homogneous real
hypersurfaces of type (A) and are a special class of Hopf hypersurfaces. 相似文献
18.
讨论了复射影空间中迷向Kaehler流形,运用活动标架法获得关于截面曲率,Ricci曲率和第二基本形式模长的Pinching定理,将相关结果作了一定的推广. 相似文献
19.
Commuting structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians 下载免费PDF全文
We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator. 相似文献