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1.
We classify all real hypersurfaces with isometric Reeb flow in the complex Grassmann manifold G
2 (ℂ
m+2
) of all 2-dimensional linear subspaces in ℂ
m+2
, m ≥ 3.
The second author was supported by Korea Research Foundation. KRF-2001-015-DP0034, Korea.
Received April 26, 2001; in revised form December 17, 2001 相似文献
2.
In this paper we construct many ruled real hypersurfaces in a nonflat quaternionic space form systematically, and in particular give an example of a homogeneous ruled real hypersurface in a quaternionic hyperbolic space. In the second half of this paper we characterize them by investigating the extrinsic shape of their geodesics. We also characterize curvature-adapted real hypersurfaces in nonflat quaternionic space forms from the same viewpoint.The first author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 14540075), Ministry of Education, Science, Sports and Culture.The second author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 14540080), Ministry of Education, Science, Sports and Culture. 相似文献
3.
Thomas Hasanis Andreas Savas-Halilaj Theodoros Vlachos 《Monatshefte für Mathematik》2005,145(4):301-305
In this paper we investigate complete minimal hypersurfaces
with at most two principal curvatures. We prove that if the squared norm S of the second fundamental form satisfies S ≥ n, then S = n and f(Mn) is a minimal Clifford torus. 相似文献
4.
Francisco Martín Cabrera 《Monatshefte für Mathematik》2006,148(1):29-50
We study SU(3)-structures induced on orientable hypersurfaces of seven-dimensional manifolds with G2-structure. Taking Gray-Hervella types for both structures into account, we relate the type of SU(3)-structure and the type of G2-structure with the shape tensor of the hypersurface. Additionally, we show how to compute the intrinsic SU(3)-torsion and the intrinsic G2-torsion by means of the exterior algebra. 相似文献
5.
The complex two-plane Grassmannian G
2(C
m+2
in equipped with both a K?hler and a quaternionic K?hler structure. By applying these two structures to the normal bundle
of a real hypersurface M in G
2(C
m+2
one gets a one- and a three-dimensional distribution on M. We classify all real hypersurfaces M in G
2
C
m+2
, m≥3, for which these two distributions are invariant under the shape operator of M.
Received 13 November 1996; in revised form 3 March 1997 相似文献
6.
We classify the real hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians SU2,m/S(U2⋅Um), m?2. Each can be described as a tube over a totally geodesic SU2,m−1/S(U2⋅Um−1) in SU2,m/S(U2⋅Um) or a horosphere whose center at infinity is singular. 相似文献
7.
Guoxin Wei 《Monatshefte für Mathematik》2006,149(4):343-350
By investigating hypersurfaces M
n
in the unit sphere S
n+1(1) with H
k
= 0 and with two distinct principal curvatures, we give a characterization of torus the
. We extend recent results of Perdomo [9], Wang [10] and Otsuki [8]. 相似文献
8.
We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations κ = F(λ) between the principal curvatures κ, λ. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(λ) = cλ2n+1. This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(λ) = cλ3. 相似文献
9.
Qiaoling Wang 《Monatshefte für Mathematik》2003,140(2):163-167
In this paper, we prove some rigidity theorems for Clifford minimal hypersurfaces in a unit sphere.Received March 18, 2002; in revised form December 25, 2002
Published online October 15, 2003 相似文献
10.
Guoxin Wei 《Monatshefte für Mathematik》2006,149(3):251-258
By investigating hypersurfaces M
n
in the unit sphere S
n+1(1) with constant mean curvature and with two distinct principal curvatures, we give a characterization of the torus S
1(a) ×
, where
. We extend recent results of Hasanis et al. [5] and Otsuki [10]. 相似文献
11.
In this paper, we show that the Boothby-Wang fibration of the Iwasawa manifold
is an unstable critical point for the energy of a distribution.
The work of the first author is partially supported by TBAG-?G/2. 相似文献
12.
Changyu Xia 《Monatshefte für Mathematik》2005,146(2):159-168
Let Sn(c) denote the n-dimensional Euclidean sphere of constant sectional curvature c and denote by CPn(c) the complex projective space of complex dimension n and of holomorphic sectional curvature c. In this paper, we obtain some characterizations of the manifolds S2(c) × S2(c′), S4(c) × S4(c′), CP2(c) × CP2(c′) by their spectrum. 相似文献
13.
We classify all real hypersurfaces with isometric Reeb flow in the complex Grassmann manifold G 2 (ℂ m+2 ) of all 2-dimensional linear subspaces in ℂ m+2 , m ≥ 3. 相似文献
14.
Bang-Yen Chen 《Monatshefte für Mathematik》2004,141(3):177-186
A submanifold of a Kaehler manifold is called a CR-warped product if it is the warped product NT ×fN of a complex submanifold NT and a totally real submanifold N. There exist many CR-warped products NT ×fN in CPh+p, h = dimCNT and p = dimRN (see [5, 6]). In contrast, we prove in this article that the situation is quite different if the holomorphic factor NT is compact. For such CR-wraped products in CPm (4), we prove the following: (1) The complex dimension m of the ambient space is at least h + p + hp. (2) If m = h + p + hp, then NT is CPh(4). We also obtain two geometric inequalities for CR-warped products in CPm with compact NT. 相似文献
15.
László Verhóczki 《Monatshefte für Mathematik》2004,141(4):323-335
In the present paper we discuss in detail the cohomogeneity one isometric actions of the Lie groups SU(3) × SU(3) and SU(3) on the exceptional compact symmetric spaces G2 and G2/SO(4), respectively. We show that the principal orbits coincide with the tubular hypersurfaces around the totally geodesic singular orbits, and the symmetric spaces G2 and G2/SO(4) can be thought of as compact tubes around SU(3) and P2, respectively. Moreover, we determine the radii of these tubes and describe the shape operators of the principal orbits. Finally, we apply these results to compute the volumes of the two symmetric spaces.The author was partially supported by the Hungarian National Science and Research Foundation OTKA T032478. 相似文献
16.
Peter A. Lesky 《Monatshefte für Mathematik》2005,144(4):297-316
Characterization of q-Orthogonal Polynomials. Im Anschluß an die Arbeit Orthogonalpolynome in x und q–x als Lösungen von reellen q-Operatorgleichungen zweiter Ordnung (Monatsh. Math. 132, 123–140 (2001); im folgenden als [4] zitiert) werden alle Möglichkeiten für q-Orthogonalpolynome in x als Lösungen von q-Operatorgleichungen zweiter Ordnung angegeben (Orthogonalität im positiv definiten Sinne). Dabei erfolgt die Numerierung der Abschnitte und die Angabe der Formel-nummern unter Einbeziehung von [4]. 相似文献
17.
We treat n-dimensional compact minimal submanifolds of complex projective space when the maximal holomorphic tangent subspace is (n − 1)-dimensional and we give a sufficient condition for such submanifolds to be tubes over totally geodesic complex subspaces.
Authors’ addresses: Mirjana Djorić, Faculty of Mathematics, University of Belgrade, Studentski trg 16, pb. 550, 11000 Belgrade,
Serbia; Masafumi Okumura, 5-25-25 Minami Ikuta, Tama-ku, Kawasaki, Japan 相似文献
18.
Toshiaki Adachi 《Monatshefte für Mathematik》2008,153(4):283-293
In this paper, we study geodesics with null structure torsions on real hypersurfaces of type A
2 in a complex space form. These geodesics give a nice family of helices of order 3 generated by Killing vector fields on the
ambient complex space form.
Author’s address: Toshiaki Adachi, Department of Mathematics, Nagoya Institute of Technology, Nagoya 466-8555, Japan 相似文献
19.
Marian Ioan Munteanu 《Monatshefte für Mathematik》2007,150(4):333-342
In this paper we study doubly warped product CR submanifolds in locally conformal K?hler manifolds, and we found a B.Y. Chen’s type inequality for the second fundamental
form of these submanifolds.
Beneficiary of a CNR-NATO Advanced Research Fellowship pos. 216.2167 Prot. n. 0015506. 相似文献
20.
In this paper, we are interested in extending the study of spherical curves in R
3 to the submanifolds in the Euclidean space R
n+p
. More precisely, we are interested in obtaining conditions under which an n-dimensional compact submanifold M of a Euclidean space R
n+p
lies on the hypersphere S
n+p−1(c) (standardly imbedded sphere in R
n+p
of constant curvature c). As a by-product we also get an estimate on the first nonzero eigenvalue of the Laplacian operator Δ of the submanifold
(cf. Theorem 3.5) as well as a characterization for an n-dimensional sphere S
n
(c) (cf. Theorem 4.1). 相似文献