共查询到20条相似文献,搜索用时 31 毫秒
1.
The aim of the present paper is to prove the non-existence of real hypersurfaces equipped with recurrent structure Jacobi operator in a non-flat complex space form. 相似文献
2.
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
3.
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
4.
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
5.
In this paper, we classify the real hypersurfaces in a non-flat complex space form with ??-parallel shape operator. 相似文献
6.
Carlos J. G. Machado Juan de Dios Pérez Imsoon Jeong Young Jin Suh 《Central European Journal of Mathematics》2011,9(3):578-582
We prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi
type. 相似文献
7.
We study curvature of Hopf hypersurfaces in a complex projective space or hyperbolic space. In particular, we prove that there are no real hypersurfaces in a non-flat complex space form whose Reeb-sectional curvature vanishes. 相似文献
8.
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
9.
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
10.
In this paper, we characterize some real hypersurfaces in a complex projective space CPn in terms of the shape operator A, the structure tensor and the Jacobi operator R. 相似文献
11.
We prove that the operator G, the closure of the first-order differential operator −d/dt+D(t) on L2(R,X), is Fredholm if and only if the not well-posed equation u′(t)=D(t)u(t), t∈R, has exponential dichotomies on R+ and R− and the ranges of the dichotomy projections form a Fredholm pair; moreover, the index of this pair is equal to the Fredholm index of G. Here X is a Hilbert space, D(t)=A+B(t), A is the generator of a bi-semigroup, B(⋅) is a bounded piecewise strongly continuous operator-valued function. Also, we prove some perturbations results and consider various examples of not well-posed problems. 相似文献
12.
Yaning Wang 《Comptes Rendus Mathematique》2018,356(7):823-829
In this paper, we prove that there are no conformally flat real hypersurfaces in nonflat complex space forms of complex dimension two provided that the structure vector field is an eigenvector field of the Ricci operator. This extends some recent results by Cho (Conformally flat normal almost contact 3-manifolds, Honam Math. J. 38 (2016) 59–69) and Kon (3-dimensional real hypersurfaces with η-harmonic curvature, in: Hermitian–Grassmannian Submanifolds, Springer, Singapore, 2017, pp. 155–164). 相似文献
13.
Summary We prove the non-existence of Einstein real hypersurfaces of quaternionic hyperbolic space.
This article was processed by the author using the IATEX style filecljour1 from Springer-Verlag. 相似文献
14.
We consider pseudodifferential operators with operator valued symbols a(x,ξ) acting on a UMD Banach space X. Assuming some regularity of Hölder type in x and Mihlin type in ξ we prove L p (? n ;X) boundedness of such operators. This result is then applied to the study of L p -maximal regularity for nonautonomous parabolic evolution equations. 相似文献
15.
Mayuko Kon 《Czechoslovak Mathematical Journal》2008,58(4):1279-1287
We give a characterization of totally η-umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition
for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator A of a real hypersurface M of a complex space form M
n
(c), c ≠ 0, n ⩾ 3, satisfies g(AX, Y) = ag(X, Y) for any X, Y ∈ T
0(x), a being a function, where T
0 is the holomorphic distribution on M, then M is a totally η-umbilical real hypersurface or locally congruent to a ruled real hypersurface. This condition for the shape operator is a
generalization of the notion of η-umbilical real hypersurfaces. 相似文献
16.
The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel. 相似文献
17.
Edgardo Alvarez-Pardo 《Semigroup Forum》2012,85(1):58-74
Let A be a densely defined, closed linear operator (which we shall call maximal operator) with domain D(A) on a Banach space X and consider closed linear operators L:D(A)???X and ??:D(A)???X (where ?X is another Banach space called boundary space). Putting conditions on L and ??, we show that the second order abstract Cauchy problem for the operator A ?? with A ?? u=Au and domain D(A ??):={u??D(A):Lu=??u} is well-posed and thus it generates a cosine operator function on the Banach space X. 相似文献
18.
Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove
that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structure
vector field is of Jacobi type. 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
20.
Summary We classifyD-Einstein real hypersurfaces of quaternionic space forms, obtaining as a consequence the non-existence of Ricci-parallel real
hypersurfaces in the quaternionic hyperbolic space.
Entrata in Redazione il 12 dicembre 1997 e, in versione riveduta, il 18 maggio 1998. 相似文献